IB Physics Semester 1 Exam Review

IB Questionbank Physics 1

1. Which of the following contains one fundamental and one derived unit?

A. ampere kilogram

B. ampere coulomb

C. joule newton

D. joule coulomb

(Total 1 mark)


2. Data analysis question.

The photograph below shows a magnified image of a dark central disc surrounded by concentric dark rings.

These rings were produced as a result of interference of monochromatic light.

The graph below shows how the ring diameter D varies with the ring number n.

The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the photograph. Error

bars for the diameter D are shown.


(a) State one piece of evidence that shows that D is not proportional to n.

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(b) On the graph above, draw the line of best-fit for the data points. (2)

(c) Theory suggests that D2 = kn.

A graph of D2 against n is shown below. Error bars are shown for the first and last data points only.


(i) Using the first graph, calculate the percentage uncertainty in D2, of the ring n = 7.

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(ii) Based on the second graph, state one piece of evidence that supports the relationship D2 = kn.

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(iii) Use the second graph to determine the value of the constant k, as well as its uncertainty.

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(iv) State the unit for the constant k.

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(Total 11 marks)

3. Which of the following will reduce random errors in an experiment?

A. Using an instrument having a greater precision

B. Checking the calibration of the instrument used

C. Checking for zero error on the instrument used

D. Repeating readings (Total 1 mark)

4. Which of the following lists two scalar quantities?

A. emf, momentum

B. emf, weight

C. impulse, kinetic energy

D. magnetic flux, kinetic energy (Total 1 mark)



The speed v of waves on the surface of deep water depends only on the wavelength λ of the waves. The data

gathered from a particular region of the Atlantic Ocean are plotted below.

The uncertainty in the speed v is ±0.30 m s–1

and the uncertainty in λ is too small to be shown on the

diagram.

(a) State, with reference to the graph,

(i) why v is not directly proportional to λ.

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(ii) the value of v for λ = 39 m.

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(b) It is suggested that the relationship between v and λ is of the form

v = a

where a is a constant. To test the validity of this hypothesis, values of v2 against λ are plotted below.

(i) Use your answer to (a)(ii) to show that the absolute uncertainty in v2 for a wavelength of 39 m is

±5 m2 s

–2.

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(ii) The absolute uncertainty in v2 for a wavelength of 2.5 m is ±1 m

2 s

–2. Using this value and the

value in (b)(i), construct error bars for v2 at the data points for

λ = 2.5 m and 39 m. (1)


(iii) State why the plotted data in (b)(ii) suggest that it is likely that v is proportional to .

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(iv) Use the graph above to determine the constant a.

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(v) Theory shows that a = π2

k. Determine a value for k.

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(Total 11 marks)


6. This question is about electrical resistance.

The graph shows the variation with temperature T of the resistance R of an electrical component.

(a) A student hypothesizes that the resistance is inversely proportional to the temperature.

Use data from the graph to show whether the hypothesis is supported.

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(b) A second student suggests that the relationship is of the form

lg R = a + T

b

where a and b are constants.

The student plots the graph below. Error bars have been included for the sake of clarity.


(i) Explain how the graph drawn could be used as evidence to support the student’s suggestion.

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(ii) Use the graph to determine the constants a and b.

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(iii) Using your answers to (b)(ii), determine a value for the resistance of the component at a

temperature of 260 K.

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(Total 11 marks)



Gillian carried out an experiment to investigate the craters formed when steel balls are dropped into sand. To

try and find the relationship between the diameter of the crater and the energy of impact of steel balls of the

same diameter, she dropped a steel ball from different heights h into sand and measured the resulting

diameter d of the crater. The data are shown plotted below.

(a) The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to be shown.

Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10). (2)

(b) Draw a best-fit line for the data points. (2)

(c) The original hypothesis, made by Gillian, was that the diameter of the crater is directly proportional to

the energy of impact of the steel balls. Explain why the data does not support this hypothesis.

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(d) Since Gillian’s data did not support her hypothesis, she researched to find alternative hypotheses. She

found that there are two theories used to predict a relationship between d and h. In order to find which

theory is best supported by the data, she processed the data in two separate ways. The processed data

are shown below.

(i) Draw a line of best-fit on each graph. (2)


(ii) State and explain which theory is best supported by the student’s data.

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(Total 11 marks)


A student performs an experiment with a paper toy that rotates as it falls slowly through the air. After release,

the paper toy quickly attains a constant vertical speed as measured over a fixed vertical distance.

The aim of the experiment was to find how the terminal speed of the paper toy varies with its weight. The

weight of the paper toy was changed by using different numbers of paper sheets in its construction.


The graph shows a plot of the terminal speed v of the paper toy (calculated from the raw data) and the

number of paper sheets n used to construct the toy. The uncertainty in v for n = 1 is shown by the error bar.

(a) The fixed distance is 0.75 m and has an absolute uncertainty of 0.01 m. The percentage uncertainty in

the time taken to fall through the fixed distance is 5 %.

(i) Calculate the absolute uncertainty in the terminal speed of the paper toy for n = 6.

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(ii) On the graph, draw an error bar on the point corresponding to n = 6. (1)


(b) On the graph, draw a line of best-fit for the data points. (1)

(c) The student hypothesizes that v is proportional to n. Use the data points for n = 2 and n = 4 from the

graph opposite to show that this hypothesis is incorrect.

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(d) Another student hypothesized that v might be proportional to n . To verify this hypothesis he plotted

a graph of v2 against n as shown below.

Explain how the graph verifies the hypothesis that v is proportional to n .

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(Total 11 marks)


9. The current, I, through a resistor is measured with a digital ammeter to be 0.10 A. The uncertainty in the

calculated value of I2 will be

A. 1 %.

B. 2 %.

C. 5 %.

D. 20 %. (Total 1 mark)

10. A body accelerates from rest with a uniform acceleration a for a time t. The uncertainty in a is 8 % and the

uncertainty in t is 4 %. The uncertainty in the speed is

A. 32 %.

B. 12 %.

C. 8 %.


11. The best estimate for the time it takes light to cross the nucleus of the hydrogen atom is

A. 10–23

s.

B. 10–20

s.

C. 10–15

s.

D. 10–7

s. (Total 1 mark)


12. The length of each side of a sugar cube is measured as 10 mm with an uncertainty of ±2 mm.

Which of the following is the absolute uncertainty in the volume of the sugar cube?

A. ±6 mm3

B. ±8 mm3

C. ±400 mm3

D. ±600 mm3

(Total 1 mark)

13. The time taken for a stone dropped from rest to fall vertically through 16 m is 2.0 s. Based on these

measurements, what is the best estimate for the acceleration of free fall?

A. 4.0 m s–2

B. 8.0 m s–2

C. 9.8 m s–2

D. 10 m s–2

(Total 1 mark)

14. The current in a resistor is measured as 2.00 A ± 0.02 A. Which of the following correctly identifies the

absolute uncertainty and the percentage uncertainty in the current?

Absolute uncertainty Percentage uncertainty

A. ± 0.02 A ±1 %

B. ± 0.01 A ± 0.5 %

C. ± 0.02 A ± 0.01 %

D. ± 0.01 A ± 0.005 %

(Total 1 mark)


15. Which of the following lists only two vector quantities?

A. mass, energy, work

B. momentum, work, speed

C. weight, force, acceleration

D. momentum, energy, displacement (Total 1 mark)

16. Which of the following is equivalent to the joule?

A. N m2

B. N m–2

C. kg m s–2

D. kg m2 s

–2

(Total 1 mark)

17. An object falls for a time of 0.25 s. The acceleration of free fall is 9.81 m s–2

. The displacement is calculated.

Which of the following gives the correct number of significant digits for the calculated value of the

displacement of the object?

A. 1

B. 2

C. 3

D. 4 (Total 1 mark)


18. A volume is measured to be 52 mm3. This volume in m

3 is

A. 5.2 × 103 m

3.

B. 5.2 × 101 m

3.

C. 5.2 × 10–1

m3.

D. 5.2 × 10–8

m3.

(Total 1 mark)

19. The masses and weights of different objects are independently measured. The graph is a plot of weight versus

mass that includes error bars.

These experimental results suggest that the

A. measurements show a significant systematic error but small random error.

B. measurements show a significant random error but small systematic error.

C. measurements are precise but not accurate.

D. weight of an object is proportional to its mass. (Total 1 mark)


20. The magnitude of the mass of the universe is of the order of

A. 1020

kg.

B. 1030

kg.

C. 1040

kg.

D. 1050

kg. (Total 1 mark)

21. Which of the following is a valid statement?

A. A measurement that is not precise can be accurate.

B. A measurement that is precise is always accurate.

C. A measurement that is not precise will always be inaccurate.

D. Repeated measurements will always increase accuracy and precision. (Total 1 mark)

22. The time elapsed since the beginning of the universe is of the order of

A. 108 s.

B. 1018

s.

C. 1028

s.

D. 1038

s. (Total 1 mark)


23. In an experiment to measure the acceleration of free fall at the surface of the Earth the following results were

obtained.

Acceleration of free fall / m s–2

7.69

7.70

7.69

7.68

7.70

The results are

A. accurate and precise.

B. inaccurate but precise.

C. accurate but imprecise.

D. inaccurate and imprecise. (Total 1 mark)

24. The order of magnitude of the weight of an apple is

A. 10–4

N.

B. 10–2

N.

C. 1 N.

D. 102 N.

(Total 1 mark)


25. The density of a metal cube is given by the expression V

Mρ where M is the mass and V is the volume of

the cube. The percentage uncertainties in M and V are as shown below.

M 12

V 4.0

The percentage uncertainty in the calculated value of the density is

A. 3.0 .

B. 8.0 .

C. 16 .

D. 48 . (Total 1 mark)

26. A car of mass 1000 kg accelerates on a straight, flat, horizontal road with an acceleration

a = 0.3 m s–2

.

The driving force F on the car is opposed by a resistive force of 500 N.

The net (resultant) force on the car is

A. 200 N.

B. 300 N.

C. 500 N.

D. 800 N. (Total 1 mark)


27. A tennis ball of mass m moving horizontally with speed u strikes a vertical tennis racket. The ball bounces

back with a horizontal speed v.

The magnitude of the change in momentum of the ball is

A. m(u + v).

B. m(u – v).

C. m(v – u).

D. zero. (Total 1 mark)

28. A brother and sister take the same time to run up a set of steps. The sister has a greater mass than her brother.

Which of the following is correct?

Has done the most work Has developed the greatest power

A. brother brother

B. brother sister

C. sister brother

D. sister sister

(Total 1 mark)


29. A nuclear power station produces 10 GW of electrical power. The power generated by the nuclear reactions

in the core of the reactor is 25 GW. The efficiency of the power station is

A. 15 %.

B. 35 %.

C. 40 %.


30. This question is about motion in a magnetic field.

An electron, that has been accelerated from rest by a potential difference of 250 V, enters a region of

magnetic field of strength 0.12 T that is directed into the plane of the page.

(a) The electron’s path while in the region of magnetic field is a quarter circle. Show that the

(i) speed of the electron after acceleration is 9.4 × 106 m s

–1.

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(ii) radius of the path is 4.5 × 10–4

m.

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(b) The diagram below shows the momentum of the electron as it enters and leaves the region of magnetic

field. The magnitude of the initial momentum and of the final momentum is 8.6 × 10–24

N s.

(i) On the diagram above, draw an arrow to indicate the vector representing the change in the

momentum of the electron. (1)

(ii) Show that the magnitude of the change in the momentum of the electron is

1.2 × 10–23

Ns.

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(iii) The time the electron spends in the region of magnetic field is 7.4 × 10–11

s.

Estimate the magnitude of the average force on the electron.

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(Total 7 marks)

31. This question is about circular motion.

A ball of mass 0.25 kg is attached to a string and is made to rotate with constant speed v along a horizontal

circle of radius r = 0.33 m. The string is attached to the ceiling and makes an angle of 30° with the vertical.

(a) (i) On the diagram above, draw and label arrows to represent the forces on the ball in the position

shown. (2)

(ii) State and explain whether the ball is in equilibrium.

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(b) Determine the speed of rotation of the ball.

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(Total 7 marks)

32. This question is about mechanics and thermal physics.

The graph shows the variation with time t of the speed v of a ball of mass 0.50 kg, that has been released

from rest above the Earth’s surface.

The force of air resistance is not negligible. Assume that the acceleration of free fall is

g = 9.81 m s–2

.

(a) State, without any calculations, how the graph could be used to determine the distance fallen.

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(b) (i) In the space below, draw and label arrows to represent the forces on the ball at

2.0 s.

(1)

(ii) Use the graph opposite to show that the acceleration of the ball at 2.0 s is approximately 4 m s–2

.

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(iii) Calculate the magnitude of the force of air resistance on the ball at 2.0 s.

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(iv) State and explain whether the air resistance on the ball at t = 5.0 s is smaller than, equal to or

greater than the air resistance at t = 2.0 s.

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(c) After 10 s the ball has fallen 190 m.

(i) Show that the sum of the potential and kinetic energies of the ball has decreased by 780 J.

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(ii) The specific heat capacity of the ball is 480 J kg–1

K–1

. Estimate the increase in the temperature

of the ball.

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(iii) State an assumption made in the estimate in (c)(ii).

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(Total 14 marks)

33. The graph shows the variation with time t of the acceleration a of an object.

Which of the following is the change in velocity of the object in the time interval 0 to 4 s?

A. –8 m s–1

B. –4 m s–1

C. +4 m s–1

D. +8 m s–1

(Total 1 mark)


34. A stone attached to a string is moving in a horizontal circle. The constant speed of the stone is v.

The diagram below shows the stone in two different positions, X and Y.

Which of the following shows the direction of the change of velocity of the stone when moving from position

X to position Y?

(Total 1 mark)


35. This question is about kinematics.

Lucy stands on the edge of a vertical cliff and throws a stone vertically upwards.

The stone leaves her hand with a speed of 15 m s–1

at the instant her hand is 80 m above the surface of the

sea. Air resistance is negligible and the acceleration of free fall is 10 m s–2

.

(a) Calculate the maximum height reached by the stone as measured from the point where it is thrown.

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(b) Determine the time for the stone to reach the surface of the sea after leaving Lucy’s hand.

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(Total 5 marks)

36. This question is about power and efficiency.

A bus is travelling at a constant speed of 6.2 m s–1

along a section of road that is inclined at an angle of 6.0°

to the horizontal.

(a) (i) The bus is represented by the black dot shown below. Draw a labelled sketch to represent the

forces acting on the bus.

(4)


(ii) State the value of the rate of change of momentum of the bus.

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(b) The total output power of the engine of the bus is 70 kW and the efficiency of the engine is 35 %.

Calculate the input power to the engine.

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(c) The mass of the bus is 8.5 × 103 kg. Determine the rate of increase of gravitational potential energy of

the bus.

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(d) Using your answer to (c) and the data in (b), estimate the magnitude of the resistive forces acting on

the bus.

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(e) The engine of the bus suddenly stops working.

(i) Determine the magnitude of the net force opposing the motion of the bus at the instant at which

the engine stops.

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(ii) Discuss, with reference to the air resistance, the change in the net force as the bus slows down.

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(Total 17 marks)

37. This question is about forces.

An athlete trains by dragging a heavy load across a rough horizontal surface.

The athlete exerts a force of magnitude F on the load at an angle of 25° to the horizontal.


(a) Once the load is moving at a steady speed, the average horizontal frictional force acting on the load is

470 N.

Calculate the average value of F that will enable the load to move at constant speed.

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(b) The load is moved a horizontal distance of 2.5 km in 1.2 hours.

Calculate

(i) the work done on the load by the force F.

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(ii) the minimum average power required to move the load.

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(c) The athlete pulls the load uphill at the same speed as in part (a).

Explain, in terms of energy changes, why the minimum average power required is greater than in

(b)(ii).

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(Total 8 marks)

38. This question is about kicking a football.

A ball is suspended from a ceiling by a string of length 7.5 m. The ball is kicked horizontally and rises to a

maximum height of 6.0 m.

(a) Assuming that the air resistance is negligible, show that the initial speed of the ball is 11 m s–1

.

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(b) The mass of the ball is 0.55 kg and the impact time of the kicker’s foot with the ball is 150 ms.

Estimate the average force exerted on the ball by the kick.

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(c) (i) Explain why the tension in the string increases immediately after the ball is kicked.

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(ii) Calculate the tension in the string immediately after the ball is kicked. Assume that the string is

vertical.

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(Total 10 marks)


39. This question is about circular motion and global warming.

(a) A car is travelling at constant speed of 18 m s–1

around a horizontal bend in the road.

The mass of the car is 1.5 × 103 kg and the bend forms part of a circle of radius

2.0 × 103 m.

(i) State why the car is accelerating.

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(ii) Determine the frictional force between the tyres of the car and the surface of the road that

produces the acceleration.

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(b) It is suggested that the use of fossil fuels to power cars has led to an enhancement of the greenhouse

effect.

(i) State the reason for this suggestion.

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(ii) Outline one mechanism by which the enhanced greenhouse effect may lead to an increase in

global warming.

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(Total 7 marks)

40. This question is about momentum, energy and power.

(a) In his Principia Mathematica Newton expressed his third law of motion as “to every action there is

always opposed an equal reaction”. State what Newton meant by this law.

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(b) A book is released from rest and falls towards the surface of Earth. Discuss how the conservation of

momentum applies to the Earth-book system.

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(c) A large swinging ball is used to drive a horizontal iron spike into a vertical wall. The centre of the ball

falls through a vertical height of 1.6 m before striking the spike in the position shown.

The mass of the ball is 3.5 kg and the mass of the spike is 0.80 kg. Immediately after striking the spike,

the ball and spike move together. Show that the

(i) speed of the ball on striking the spike is 5.6 m s–1

.

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(ii) energy dissipated as a result of the collision is about 10 J.

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(d) As a result of the ball striking the spike, the spike is driven a distance 7.3 × 10–2

m into the wall.

Calculate, assuming it to be constant, the friction force F between the spike and wall.

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(e) The machine that is used to raise the ball has a useful power output of 18 W. Calculate how long it

takes for the machine to raise the ball through a height of 1.6 m.

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(Total 15 marks)

41. In 1997 a high-speed car of mass 1.1 × 104 kg achieved the world land speed record. The car accelerated

uniformly in two stages as shown in the table. The car started from rest.

Time / s Speed attained at end of stage / m s–1

Stage 1 0.0 – 4.0 44

Stage 2 4.0 – 12 280


Use the data to calculate the

(a) average acceleration of the car in stage 1.

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(b) average net force required to accelerate the car in stage 2.

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(c) total distance travelled by the car in 12 s.

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(Total 6 marks)


42. This question is about a simple pendulum.

(a) A pendulum consists of a bob suspended by a light inextensible string from a rigid support. The

pendulum bob is moved to one side and then released. The sketch graph shows how the displacement

of the pendulum bob undergoing simple harmonic motion varies with time over one time period.

On the sketch graph above,

(i) label with the letter A a point at which the acceleration of the pendulum bob is a maximum. (1)

(ii) label with the letter V a point at which the speed of the pendulum bob is a maximum. (1)

(b) Explain why the magnitude of the tension in the string at the midpoint of the oscillation is greater than

the weight of the pendulum bob.

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......................................................................................................................................

...................................................................................................................................... (3)


(c) The pendulum bob is moved to one side until its centre is 25 mm above its rest position and then

released.

(i) Show that the speed of the pendulum bob at the midpoint of the oscillation is 0.70 m s–1

.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) The mass of the pendulum bob is 0.057 kg. The centre of the pendulum bob is 0.80 m below the

support. Calculate the magnitude of the tension in the string when the pendulum bob is vertically

below the point of suspension.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(d) The point of suspension of the pendulum bob is moved from side to side with a small amplitude and at

a variable driving frequency f.

For each value of the driving frequency a steady constant amplitude A is reached. The oscillations of

the pendulum bob are lightly damped.

(i) On the axes below, sketch a graph to show the variation of A with f.

(2)

(ii) Explain, with reference to the graph in (d)(i), what is meant by resonance.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(e) The pendulum bob is now immersed in water and the variable frequency driving force in (d) is again

applied. Suggest the effect this immersion of the pendulum bob will have on the shape of your graph in

(d)(i).

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 16 marks)

43. This question is about collisions.

(a) State the principle of conservation of momentum.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) In an experiment, an air-rifle pellet is fired into a block of modelling clay that rests on a table.

(not to scale)

The air-rifle pellet remains inside the clay block after the impact.

As a result of the collision, the clay block slides along the table in a straight line and comes to rest.

Further data relating to the experiment are given below.

Mass of air-rifle pellet = 2.0 g

Mass of clay block = 56 g

Velocity of impact of air-rifle pellet = 140 m s–1

Stopping distance of clay block = 2.8 m

(i) Show that the initial speed of the clay block after the air-rifle pellet strikes it is

4.8 m s–1

.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) Calculate the average frictional force that the surface of the table exerts on the clay block whilst

the clay block is moving.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(c) Discuss the energy transformations that occur in the clay block and the air-rifle pellet from the moment

the air-rifle pellet strikes the block until the clay block comes to rest.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(d) The clay block is dropped from rest from the edge of the table and falls vertically to the ground. The

table is 0.85 m above the ground. Calculate the speed with which the clay block strikes the ground.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 13 marks)


44. This question is about impulse.

(a) A net force of magnitude F acts on a body. Define the impulse I of the force.

......................................................................................................................................

...................................................................................................................................... (1)

(b) A ball of mass 0.0750 kg is travelling horizontally with a speed of 2.20 m s–1

. It strikes a vertical wall

and rebounds horizontally.

Due to the collision with the wall, 20 % of the ball’s initial kinetic energy is dissipated.

(i) Show that the ball rebounds from the wall with a speed of 1.97 m s–1

.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Show that the impulse given to the ball by the wall is 0.313 N s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(c) The ball strikes the wall at time t = 0 and leaves the wall at time t = T.

The sketch graph shows how the force F that the wall exerts on the ball is assumed to vary with time t.

The time T is measured electronically to equal 0.0894 s.

Use the impulse given in (b)(ii) to estimate the average value of F.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(Total 9 marks)

45. This question is about motion of a ball falling in oil.

(a) Distinguish between average speed and instantaneous speed.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) A small steel ball of mass M is dropped from rest into a long vertical tube that contains oil.

The sketch graph shows how the speed v of the ball varies with time t.

Explain how you would use the graph to find the average speed of the ball between t = 0 and t = t1.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c) The gradient of the graph at t = t1 is k. Deduce an expression in terms of k, M and g, the acceleration of

free fall, for the magnitude of the frictional force F acting on the ball at t = t1.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)


(d) State and explain the magnitude of the frictional force acting on the ball at t = t2.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 11 marks)

46. This question is about dynamics and energy.

A bullet of mass 32 g is fired from a gun. The graph shows the variation of the force F on the bullet with time

t as it travels along the barrel of the gun.

The bullet is fired at time t = 0 and the length of the barrel is 0.70 m.


(a) State and explain why it is inappropriate to use the equation s = ut + 2

21 at to calculate the

acceleration of the bullet.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Use the graph to

(i) determine the average acceleration of the bullet during the final 2.0 ms of the graph.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) show that the change in momentum of the bullet, as the bullet travels along the length of the

barrel, is approximately 9 N s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(c) Use the answer in (b)(ii) to calculate the

(i) speed of the bullet as it leaves the barrel.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) average power delivered to the bullet.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(d) Use Newton’s third law to explain why a gun will recoil when a bullet is fired.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 15 marks)


47. This question is about force and energies.

(a) A system consists of a bicycle and cyclist travelling at a constant velocity along a horizontal road.

(i) State the value of the net force acting on the cyclist.

........................................................................................................................... (1)

(ii) On the diagram draw labelled arrows to represent the vertical forces acting on the bicycle. (2)

(iii) With reference to the horizontal forces acting on the system, explain why the system is

travelling at constant velocity.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(b) The total resistive force acting on the system is 40 N and its speed is 8.0 m s–1

. Calculate the useful

power output of the cyclist.

......................................................................................................................................

...................................................................................................................................... (1)

(c) The cyclist stops pedalling and the system comes to rest. The total mass of the system is 70 kg.

(i) Calculate the magnitude of the initial acceleration of the system.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Estimate the distance taken by the system to come to rest from the time the cyclist stops

pedalling.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) State and explain one reason why your answer to (c)(ii) is only an estimate.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 12 marks)


48. Mechanical power

(a) Define power.

...................................................................................................................................

................................................................................................................................... (1)

(b) A car is travelling with constant speed v along a horizontal straight road. There is a total resistive force

F acting on the car.

Deduce that the power P to overcome the force F is P = Fv.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) A car drives up a straight incline that is 4.8 km long. The total height of the incline is 0.30 km.

The car moves up the incline at a steady speed of 16 m s–1

. During the climb, the average friction force

acting on the car is 5.0 102 N. The total weight of the car and the driver is 1.2 10

4 N.

(i) Determine the time it takes the car to travel from the bottom to the top of the incline.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)


(ii) Determine the work done against the gravitational force in travelling from the bottom to the top

of the incline.

......................................................................................................................... (1)

(iii) Using your answers to (c)(i) and (c)(ii), calculate a value for the minimum power output of the

car engine needed to move the car from the bottom to the top of the incline.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (4)

(d) From the top of the incline, the road continues downwards in a straight line. At the point where the

road starts to go downwards, the driver of the car in (c), stops the car to look at the view. In continuing

his journey, the driver decides to save fuel. He switches off the engine and allows the car to move

freely down the hill. The car descends a height of 0.30 km in a distance of 6.4 km before levelling out.

The average resistive force acting on the car is 5.0 102 N.


Estimate

(i) the acceleration of the car down the incline.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (5)

(ii) the speed of the car at the bottom of the incline.

.........................................................................................................................

......................................................................................................................... (2)

(e) In fact, for the last few hundred metres of its journey down the hill, the car travels at constant speed.

State the value of the frictional force acting on the car whilst it is moving at constant speed.

................................................................................................................................... (1)

(Total 18 marks)


49. This question is about electrical resistance of the metal mercury.

The resistance R of a sample of mercury was measured as a function of the temperature T of the sample. The

sample was cooled and data points were taken at temperature intervals of 0.2 K. The uncertainties in R and T

are too small to be shown on the graph.

The hypothesis is that resistance is proportional to absolute temperature for temperatures greater than 4.5 K.

(a) (i) Suggest whether the data supports the hypothesis.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Draw a line of best fit through the data. (2)

(b) State the value of R for which the rate of change of resistance of the sample with temperature is least.

...................................................................................................................................... (1)


(c) At a temperature TC the resistance suddenly becomes zero.

(i) Use the graph to determine the possible range of the temperature TC.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(ii) State, to the correct number of significant figures, the value of TC and its uncertainty.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) Outline how the temperature TC could be measured more precisely.

...........................................................................................................................

........................................................................................................................... (1)

(d) Outline two reasons why you could not use the data to determine an accurate value for R at room

temperature.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 10 marks)


50. This question is about liquid flow.

The diagram shows a storage container for liquids.

The container is filled from above. The distance between the base of the container and the ground is h0.


The container, which is initially empty, is then filled at a constant rate. The height h of the liquid surface

above the ground is measured as a function of time t. The results of the measurements are shown plotted

below.

(a) Draw a best-fit line for the data. (1)

(b) It is hypothesized that h is directly proportional to t. State and explain whether this hypothesis is

correct for the periods

(i) t = 0 to t = 120 s.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)


(ii) t > 120 s.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(c) Use data from the graph to determine the value of h0.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) The area of the base of the container is 1.8 m2. Deduce that the volume of liquid entering the storage

container each second is approximately 0.02 m3 s

–1.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(e) The container is completely filled after 850 s. Calculate the total volume of the container.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)


(f) The empty container is now filled at half the rate in (d). Using the axes, sketch a graph to show the

variation of h with t in the range t = 0 to t = 900 s.

(2)

(Total 11 marks)

51. A skydiver of mass 80 kg falls vertically with a constant speed of 50 m s–1

. The upward force acting on the

skydiver is approximately

A. 0 N.

B. 80 N.

C. 800 N.



52. Joseph runs along a long straight track. The variation of his speed v with time t is shown below.

After 25 seconds Joseph has run 200 m. Which of the following is correct at 25 seconds?

Instantaneous speed / m s–1

Average speed / m s–1

A. 8 m s–1

8 m s–1

B. 8 m s–1

10 m s–1

C. 10 m s–1

8 m s–1

D. 10 m s–1

10 m s–1

(Total 1 mark)

53. A cyclist rides around a circular track at a uniform speed. Which of the following correctly gives the net

horizontal force on the cyclist at any given instant of time?

Net horizontal force along

direction of motion

Net horizontal force normal to

direction of motion

A. zero zero

B. zero non zero

C. non zero zero

D. non zero non zero

(Total 1 mark)


54. A car accelerates from rest. The acceleration increases with time. Which graph shows the variation with time

t of the speed v of the car?

(Total 1 mark)

55. Which of the following is the condition for a body to be in translational equilibrium?

A. The resultant force on the body in any direction is zero.

B. The velocity of the body in any direction is zero.

C. No external force is acting on the body.

D. No work is done on the body. (Total 1 mark)


56. The graph shows the variation with force F of the extension s of a spring.

The work done in changing the extension of the spring from 3.0 cm to 6.0 cm is

A. 15 N cm.

B. 30 N cm.

C. 45 N cm.

D. 60 N cm. (Total 1 mark)

57. A wooden block is sliding down an inclined plane at constant speed. The magnitude of the frictional force

between the block and the plane is equal to

A. zero.

B. the magnitude of the weight of the block.

C. the magnitude of the component of weight of the block parallel to the plane.

D. the magnitude of the component of the normal reaction parallel to the plane. (Total 1 mark)


58. Which of the following is a correct statement of Newton’s second law of motion?

A. A force acting on a body is proportional to the mass of the body.

B. The rate of change of momentum of a body is equal to the net external force acting on the body.

C. The momentum of a body is proportional to the net external force acting on the body.

D. A force acting on a body is proportional to the acceleration of the body. (Total 1 mark)

59. A ball of weight W is travelling horizontally towards a vertical wall. It strikes the wall and rebounds

horizontally. The change in the magnitude of the momentum of the ball is ∆p. Which of the following is the

magnitude of the impulse that the ball imparts to the wall?

A. W + ∆p

B. W – ∆p

C. W

D. ∆p (Total 1 mark)


60. Two objects undergo an inelastic collision. Which of the following is correct in respect of both the

conservation of momentum and the conservation of total energy of the system?

Momentum Total energy

A. conserved not conserved

B. conserved conserved

C. not conserved not conserved

D. not conserved conserved

(Total 1 mark)

61. A particle P is moving anti-clockwise with constant speed in a horizontal circle.

Which diagram correctly shows the direction of the velocity v and acceleration a of the particle P in the

position shown?

(Total 1 mark)


62. Samantha walks along a horizontal path in the direction shown. The curved part of the path is a semi-circle.

The magnitude of her displacement from point P to point Q is approximately

A. 2 m.

B. 4 m.

C. 6 m.

D. 8 m. (Total 1 mark)

63. Which of the following may be determined from a speed-time graph?

A. Displacement

B. Distance

C. Power

D. Force (Total 1 mark)


64. Stephen pushes two boxes P and Q, that stay in contact, along a rough table, with a force F of 30 N.

Box P has a mass of 2.0 kg and box Q has a mass of 4.0 kg. Both boxes move with constant speed.

The resultant force on box Q is

A. 0 N.

B. 5.0 N.

C. 15 N.



65. A ball moves along the inside of a horizontal semi-circular ring as shown. The diagram is a view from above.

Which arrow represents the direction of the average force on the ball?

(Total 1 mark)


66. A ball is thrown vertically upwards and comes down again. Air resistance is negligible. Which of the

following graphs shows how the gravitational potential energy EP varies with time t?

(Total 1 mark)

67. A pump extracts water from a well of depth h at a constant rate of R kg s–1

. What is the power required to

raise the water?

A. gh

R

B. Rgh

C. h

Rg

D. R

hg

(Total 1 mark)


68. A raindrop falling from rest at time t = 0 reaches terminal velocity. Which graph best represents how the

speed v varies with time t?

(Total 1 mark)


69. The graph shows how the displacement d of an object varies with time t. The tangent to the curve at time t1 is

also shown.

Which of the following gives the speed of the object at point P?

A. the gradient at P

B. the shaded area

C. Pat gradient

1

D. 1

1

t

d

(Total 1 mark)


70. A ball falls vertically and bounces off the ground. Immediately before impact with the ground the speed of

the ball is u. Immediately after leaving the ground the speed is v.

Which of the following expressions is the ratio of collision beforey immediatelenergy kinetic

collisionon lost energy kinetic?

A. u

v

B. u

v1

C.

2

u

v

D.

2

1

u

v

(Total 1 mark)


71. A railway engine of mass m moves along a horizontal track with uniform speed v. The total resistive force

acting on the engine is F.

Which of the following is the power of the engine?

A. mv

F

B. Fv

C. F

mv

D. F

v

(Total 1 mark)

72. A ball is tied to a string and rotated at a uniform speed in a vertical plane. The diagram shows the ball at its

lowest position. Which arrow shows the direction of the net force acting on the ball?

(Total 1 mark)


73. A gas atom strikes a wall with speed v at an angle θ to the normal to the wall. The atom rebounds at the same

speed v and angle θ.

Which of the following gives the magnitude of the momentum change of the gas atom?

A. zero

B. 2mv sinθ

C. 2mv

D. 2mv cosθ (Total 1 mark)

74. A skydiver jumped out of an airplane. On reaching a terminal speed of 60 m s–1

, she opened her parachute.

Which of the following describes her motion after opening her parachute?

A. She went upwards for a short time, before falling to Earth at a speed of 60 m s–1

.

B. She continued downwards at 60 m s–1

, but hit the ground with less force.

C. She continued to fall but reached a new terminal speed of less than 60 m s–1

.

D. She went upwards for a short time, before falling to Earth at a speed of less than 60 m s–1

. (Total 1 mark)


75. The graph is a speed versus time graph for an object that is moving in a straight line.

The distance travelled by the object during the first 4.0 seconds is

A. 80 m.

B. 40 m.

C. 20 m.



76. The diagram shows a girl attempting (but failing) to lift a heavy suitcase of weight W. The magnitude of the

vertical upwards pull of the girl on the suitcase is P and the magnitude of the vertical reaction of the floor on

the suitcase is R.

Which equation correctly relates W, P and R?

A. W = P + R

B. W > P + R

C. W < P + R

D. W = P = R (Total 1 mark)

77. Objects A and B collide together. They end up joined together and stationary. During the collision, a force +F

is exerted on object A by object B. According to Newton’s third law, there will also be a force of

A. –F acting on object B.

B. –F acting on object A.

C. +F acting on object B.

D. +F acting on object A. (Total 1 mark)


78. A lift (elevator) is operated by an electric motor. It moves between the 10th floor and the 2nd floor at a

constant speed. One main energy transformation during this journey is

A. gravitational potential energy → kinetic energy.

B. electrical energy → kinetic energy.

C. kinetic energy → thermal energy.

D. electrical energy → thermal energy. (Total 1 mark)

79. A communications satellite is moving at a constant speed in a circular orbit around Earth. At any given

instant in time, the resultant force on the satellite is

A. zero.

B. equal to the gravitational force on the satellite.

C. equal to the vector sum of the gravitational force on the satellite and the centripetal force.

D. equal to the force exerted by the satellite’s rockets. (Total 1 mark)


80. A ball, initially at rest, is dropped in the air from a great height. Air resistance is not negligible.

Which of the following graphs best shows the variation with time t of the acceleration a of the ball?

(Total 1 mark)


81. The graph below shows the variation with time t of the velocity v of an object moving along a straight line.

The displacement of the object between t = 0 s and t = 6.0 s is

A. 2.0 m.

B. 12 m.

C. 20 m.



82. A constant force of magnitude F is applied to a mass m for a time interval ∆t. The magnitude of the impulse

given to the mass equals

A. m

F.

B. t

F

.

C. F∆t.

D. m

tF.

(Total 1 mark)

83. Two carts of different mass m and M are connected by a spring. They are pushed together such that the spring

is compressed.

After the carts are released, the cart of mass m moves with velocity v. The change in the momentum of mass

M is

A. mv.

B. –mv.

C. Mv.

D. –Mv. (Total 1 mark)


84. A lamp of weight W is suspended by a wire fixed to the ceiling. With reference to Newton’s third law of

motion, the force that is equal and opposite to W is the

A. tension in the wire.

B. force applied by the ceiling.

C. force exerted by the lamp on the Earth.

D. force exerted by the Earth on the lamp. (Total 1 mark)

85. A constant force acts on a mass that is initially at rest. Which of the following graphs best shows how the

kinetic energy EK of the mass changes with the work W done on the mass? Friction is negligible.

(Total 1 mark)


86. Two balls of different mass are dropped from the top of a tall building one after the other. The distance

between the balls

A. increases with time.

B. depends on the initial velocity only.

C. remains constant.

D. depends on the mass of the balls. (Total 1 mark)


87. The graph shows how the velocity of a particle varies with time.

Which of the following graphs correctly shows how the acceleration of the particle varies with time?

(Total 1 mark)


88. An aircraft is flying at constant speed in a horizontal circle. Which of the following diagrams best illustrates

the forces acting on the aircraft in the vertical plane?

(Total 1 mark)

89. For a particle moving at constant speed in a horizontal circle, the work done by the centripetal force is

A. zero.

B. directly proportional to the particle mass.

C. directly proportional to the particle speed.

D. directly proportional to the (particle speed)2.

(Total 1 mark)


90. A vehicle is driven up a hill at constant speed. Which of the following best describes the energy changes

involved?

A. Chemical energy is converted into gravitational potential energy.

B. Chemical energy is converted into gravitational potential energy, sound and thermal energy.

C. Gravitational potential energy is converted into chemical energy.

D. Gravitational potential energy is converted into chemical energy, sound and thermal energy. (Total 1 mark)

91. A rubber ball, travelling in a horizontal direction, strikes a vertical wall. It rebounds at right angles to the

wall. The graph below illustrates the variation of the ball’s momentum p with time t when the ball is in

contact with the wall.

Which of the following statements is true?

A. The shaded area is equal to the force exerted by the wall on the ball.

B. The shaded area is equal to the force exerted by the ball on the wall.

C. The gradient is equal to the force exerted by the wall on the ball.

D. The gradient is equal to the force exerted by the ball on the wall. (Total 1 mark)


92. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical

displacement d of the ball.

Which of the following gives the final displacement after time T and the average speed between time t = 0

and time t = T?

Displacement Average speed

A. 0 0

B. 0

T

D2

C. 2D

T

D2

D. 2D 0

(Total 1 mark)


93. A general expression for Newton’s second law of motion is

.t

pF

What condition is applied so that the law may be expressed in the form F = ma?

A. The mass m is constant.

B. The acceleration a is constant.

C. The force F is constant.

D. The direction of the force F is constant. (Total 1 mark)

94. Mandy stands on a weighing scale inside a lift (elevator) that accelerates vertically upwards as shown in the

diagram below. The forces on Mandy are her weight W and the reaction force from the scale R.

The reading of the scale is

A. R + W.

B. W.

C. R.

D. R – W. (Total 1 mark)


95. Two spheres of masses m1 and m2 are moving towards each other along the same straight-line with speeds v1

and v2 as shown.

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a

result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 − m2v2

D. m2v2 − m1v1

(Total 1 mark)


96. Light travels from air into glass as shown below.

What is the refractive index of glass?

A. S

P

sin

sin

B. R

Q

sin

sin

C. R

P

sin

sin

D. S

Q

sin

sin

(Total 1 mark)


97. Which of the following electromagnetic waves has a frequency greater than that of visible light?

A. Ultraviolet

B. Radio

C. Microwaves

D. Infrared (Total 1 mark)

98. This question is about simple harmonic oscillations.

A longitudinal wave travels through a medium from left to right.

Graph 1 shows the variation with time t of the displacement x of a particle P in the medium.

Graph 1

(a) For particle P,

(i) state how graph 1 shows that its oscillations are not damped.

........................................................................................................................... (1)


(ii) calculate the magnitude of its maximum acceleration.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) calculate its speed at t = 0.12 s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iv) state its direction of motion at t = 0.12 s.

........................................................................................................................... (1)


(b) Graph 2 shows the variation with position d of the displacement x of particles in the medium at a

particular instant of time.

Graph 2

Determine for the longitudinal wave, using graph 1 and graph 2,

(i) the frequency.

........................................................................................................................... (2)

(ii) the speed.

........................................................................................................................... (2)


Graph 2 – reproduced to assist with answering (c)(i).

(c) The diagram shows the equilibrium positions of six particles in the medium.

(i) On the diagram above, draw crosses to indicate the positions of these six particles at the instant

of time when the displacement is given by graph 2. (3)


(ii) On the diagram above, label with the letter C a particle that is at the centre of a compression. (1)

(Total 14 marks)

99. An object is undergoing simple harmonic motion with light damping. The natural frequency of oscillation of

the object is f0. A periodic force of frequency f is applied to the object. Which of the following graphs best

shows how the amplitude a of oscillation of the object varies with f?

(Total 1 mark)


100. The graph shows measurements of the height h of sea level at different times t in the Bay of Fundy.

Which of the following gives the approximate amplitude and period of the tides?

Amplitude Period

A. 6.5 m 6 hours

B. 13 m 12 hours

C. 6.5 m 12 hours

D. 13 m 6 hours

(Total 1 mark)

101. This question is about simple harmonic motion (SHM) and a wave in a string.

(a) By reference to simple harmonic motion, state what is meant by amplitude.

......................................................................................................................................

...................................................................................................................................... (1)


(b) A liquid is contained in a U-tube.

Diagram 1 Diagram 2

The pressure on the liquid in one side of the tube is increased so that the liquid is displaced as shown in

diagram 2. When the pressure is suddenly released the liquid oscillates.

The damping of the oscillations is small.

(i) Describe what is meant by damping.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) The displacement of the liquid surface from its equilibrium position is x. The acceleration a of

the liquid in the tube is given by the expression

a = xl

g2

where g is the acceleration of free fall and l is the total length of the liquid column.

The total length of the liquid column in the tube is 0.32 m. Determine the period of oscillation.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) A wave is travelling along a string. The string can be modelled as a single line of particles and each

particle executes simple harmonic motion. The period of oscillation of the particles is 0.80 s.

The graph shows the displacement y of part of the string at time t = 0. The distance along the string is

d.

(i) On the graph, draw an arrow to show the direction of motion of particle P at the point marked on

the string. (1)


(ii) Determine the magnitude of the velocity of particle P.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(iii) Show that the speed of the wave is 5.0 m s–1

.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iv) On the graph above, label with the letter X the position of particle P at t = 0.40 s. (1)

(Total 15 marks)


102. This question is about water wave motion.

A small sphere, mounted at the end of a vertical rod, dips below the surface of shallow water in a tray. The

sphere is driven vertically up and down by a motor attached to the rod.

The oscillations of the sphere produce travelling waves on the surface of the water.

(a) The diagram shows how the displacement of the water surface at a particular instant in time varies with

distance from the sphere. The period of oscillation of the sphere is 0.027 s.

Use the diagram to calculate, for the wave,

(i) the amplitude.

...........................................................................................................................

........................................................................................................................... (1)


(ii) the wavelength.

...........................................................................................................................

........................................................................................................................... (1)

(iii) the frequency.

...........................................................................................................................

........................................................................................................................... (1)

(iv) the speed.

...........................................................................................................................

........................................................................................................................... (1)

(b) The wave moves from region A into a region B of shallower water. The waves move more slowly in

region B. The diagram (not to scale) shows some of the wavefronts in region A.


(i) With reference to a wave, distinguish between a ray and a wavefront.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) The angle between the wavefronts and the interface in region A is 60°. The refractive index AnB

is 1.4.

Determine the angle between the wavefronts and the interface in region B.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) On the diagram above, construct three lines to show the position of three wavefronts in region

B. (2)


(c) Another sphere is dipped into the water. The spheres oscillate in phase. The diagram shows some lines

in region A along which the disturbance of the water surface is a minimum.

(i) Outline how the regions of minimum disturbance occur on the surface.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(ii) The frequency of oscillation of the spheres is increased.

State and explain how this will affect the positions of minimum disturbance.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 15 marks)

103. This question is about oscillations and waves.

(a) A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1.

The length of wood below the surface is d. The wood is pushed vertically downwards a distance A

such that a length of wood is still above the water surface as shown in diagram 2. The wood is then

released and oscillates vertically. At the instant shown in diagram 3, the wood is moving downwards

and the length of wood beneath the surface is d + x.

(i) On diagram 3, draw an arrow to show the direction of the acceleration of the wood. (1)


(ii) The acceleration a of the wood (in m s–2

) is related to x (in m) by the following equation.

a = xl

14

Explain why this equation shows that the wood is executing simple harmonic motion.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is 0.70 m.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(b) The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below, sketch a graph to

show how the velocity v of the wood varies with time over one period of oscillation.

(1)

(c) The distance A that the wood is initially pushed down is 0.12 m.

(i) Calculate the magnitude of the maximum acceleration of the wood.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) On your sketch graph in (b) label with the letter P one point where the magnitude of the

acceleration is a maximum. (1)


(d) The oscillations of the wood generate waves in the water of wavelength 0.45 m.

The graph shows how the displacement D, of the water surface at a particular distance from the wood

varies with time t.

Using the graph, calculate the

(i) speed of the waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(iii) ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s

...........................................................................................................................

........................................................................................................................... (1)

(Total 15 marks)

104. This question is about simple harmonic motion and waves.

(a) A particle of mass m that is attached to a light spring is executing simple harmonic motion in a

horizontal direction.

State the condition relating to the net force acting on the particle that is necessary for it to execute

simple harmonic motion.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) The graph shows how the kinetic energy EK of the particle in (a) varies with the displacement x of the

particle from equilibrium.


(i) Using the axes above, sketch a graph to show how the potential energy of the particle varies

with the displacement x. (2)

(ii) The mass of the particle is 0.30 kg. Use data from the graph to show that the frequency f of

oscillation of the particle is 2.0 Hz.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(c) The particles of a medium M1 through which a transverse wave is travelling, oscillate with the same

frequency and amplitude as that of the particle in (b).

(i) Describe, with reference to the propagation of energy through the medium, what is meant by a

transverse wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) The speed of the wave is 0.80 m s–1

. Calculate the wavelength of the wave.

...........................................................................................................................

........................................................................................................................... (1)


(d) The diagram shows wavefronts of the waves in (c) incident on a boundary XY between medium M1

and another medium M2.

The angle between the normal, and the direction of travel of the wavefronts is 30°.

(i) The speed of the wave in M1 is 0.80 m s–1

. The speed of the waves in M2 is

1.2 m s–1

.

Calculate the angle between the direction of travel of the wavefronts in M2 and the normal.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) On the diagram, sketch the wavefronts in M2.

(1)

(Total 15 marks)


105. A battery of internal resistance 2 Ω is connected to an external resistance of 10 Ω. The current is 0.5 A.

What is the emf of the battery?

A. 1.0 V

B. 5.0 V

C. 6.0 V

D. 24.0 V (Total 1 mark)


106. In the circuit below, which of the following will cause the greatest increase in the reading of the voltmeter?

A. An increase in temperature

B. An increase in light intensity

C. A decrease in temperature

D. A decrease in light intensity (Total 1 mark)

107. This question is about electric circuits.

(a) Define

(i) electromotive force (emf ) of a battery.

...........................................................................................................................

........................................................................................................................... (1)


(ii) electrical resistance of a conductor.

...........................................................................................................................

........................................................................................................................... (1)

(b) A battery of emf ε and negligible internal resistance is connected in series to two resistors. The current

in the circuit is I.

(i) State an equation giving the total power delivered by the battery.

........................................................................................................................... (1)

(ii) The potential difference across resistor R1 is V1 and that across resistor R2 is V2.

Using the law of the conservation of energy, deduce the equation below.

ε = V1 + V2

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(c) The graph shows the I-V characteristics of two conductors, X and Y.

On the axes below, sketch graphs to show the variation with potential difference V of the resistance of

conductor X (label this graph X) and conductor Y (label this graph Y).

You do not need to put any numbers on the vertical axis.

(3)


(d) The conductors in (c) are connected in series to a battery of emf ε and negligible internal resistance.

The power dissipated in each of the two resistors is the same.

Using the graph given in (c),

(i) determine the emf of the battery.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) calculate the total power dissipated in the circuit.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 12 marks)


108. Two electrodes, separated by a distance d, in a vacuum are maintained at a constant potential difference. An

electron, accelerated from one electrode to the other, gains kinetic energy Ek. The distance between the

electrodes is now changed to 3

1d.

What is the gain in kinetic energy of an electron that is accelerated from one electrode to the other?

A. 3

kE

B. Ek

C. 3 Ek

D. 9 Ek

(Total 1 mark)

109. The graph shows the I–V characteristics of two resistors.

When resistors X and Y are connected in series, the current in the resistors is 2.0 A. What is the resistance of

the series combination of X and Y?

A. 7.0 Ω

B. 1.3 Ω

C. 1.1 Ω

D. 0.14 Ω (Total 1 mark)



(a) A resistor of resistance 1.5 Ω is made from copper wire of radius 0.18 mm. The resistivity of copper is

1.7 × 10–8

Ω m. Determine the length of copper wire used to make the resistor.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) The manufacturer of the resistor in (a) guarantees that the resistance is within 10 % of 1.5 Ω , provided

that the power dissipation in the resistor does not exceed 1.0 W.

(i) Suggest why the resistance of the resistor might be greater than 1.65 Ω if the power dissipation

in the resistor is greater than 1.0 W.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Show that, for a power dissipation of 1.0 W, the current in a resistor of resistance 1.5 Ω is 0.82

A.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)


(iii) The 1.5 Ω resistor is connected in series with a variable resistor and battery of emf 6.0 V and

internal resistance 1.8 Ω.

Estimate the resistance R of the variable resistor that will limit the current to 0.82 A.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 8 marks)

111. This question is about an electrical heater.

An electrical heater consists of two heating elements E1 and E2. The elements are connected in parallel. Each

element has a switch and is connected to a supply of emf 240 V. The supply has negligible internal

resistance.

Element E1 is made from wire that has a cross-sectional area of 6.8 × 10–8

m2. The resistivity of the wire at

the operating temperature of the element is 1.1 × 10–6

Ωm.


(a) (i) The total length of wire is 4.5 m. Show that the resistance of E1 is 73 Ω.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the power output of E1 with only this element connected to the supply.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) Element E2 is made of wire of the same cross-section and material as E1. The length of wire

used to make E2 is 1.5 m. Determine the total power output when both E1 and E2 are connected

to the supply.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iv) With reference to the power output, explain why it would be inappropriate to connect the

heating elements in series.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(b) Each element in the electrical heater is wound as a coil as shown.

Each turn of the coil may be considered to act as a current-carrying long straight wire.

(i) On the diagram, draw the magnetic field around a current-carrying long straight wire. The arrow

shows the direction of the current.

(3)

(ii) State and explain whether the turns of wire will attract or repel one another.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 15 marks)


112. This question is about electrical resistance and electric circuits.

(a) Define resistance and state Ohm’s law.

Resistance: ...................................................................................................................

......................................................................................................................................

Ohm’s law: ..................................................................................................................

...................................................................................................................................... (2)

(b) A resistor made from a metal oxide has a resistance of 1.5 Ω. The resistor is in the form of a cylinder

of length 2.2 × 10–2

m and radius 1.2 × 10–3

m. Calculate the resistivity of the metal oxide.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) The manufacturer of the resistor in (b) guarantees its resistance to be within ±10 % of 1.5 Ω provided

the power dissipation in the resistor does not exceed 1.0 W. Calculate the maximum current in the

resistor for the power dissipation to be equal to 1.0 W.

......................................................................................................................................

...................................................................................................................................... (2)


(d) The resistance of each of the resistors in the circuit below is measured to be 1.5 Ω with an accuracy of

±10 %.

The cell has an emf of 2.0 V and negligible internal resistance.

(i) Define emf.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Determine the minimum and the maximum power that could be dissipated in this circuit.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 10 marks)


113. (a) Draw the complete diagram of the circuit that uses a potential divider, ammeter, voltmeter and cell to

measure the current-voltage characteristics for component X.

(3)


(b) The graph shows the current-voltage characteristics for the component X.

Component X is now connected across the terminals of a cell of emf 2.0 V and negligible internal

resistance. Use the graph to show that the resistance of X is 0.83 Ω.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) A resistor of constant resistance 1.0 Ω is connected in series with the cell in (b) and with X. Use the

graph to deduce that the current in the circuit is 1.3 A.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 8 marks)


114. This question is about electric fields and electric circuits.

(a) Two parallel, charged metal plates A and B are in a vacuum.

At a particular instant an electron is at point P.

On the diagram, draw

(i) the electric field pattern due to the plates. (3)

(ii) an arrow to represent the direction of the force on the electron at P. (1)

(b) The acceleration of the electron at P is 8.8 × 1014

m s–2

. Determine the magnitude of the electric field

strength at the point P.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c) The electric potential energy of the electron changes by 1.9 × 10–17

J as it moves from one plate to the

other. Show that the potential difference between the plates is 120 V.

......................................................................................................................................

...................................................................................................................................... (1)


(d) A resistor R and a filament lamp L are connected in series with a battery. The battery has an emf of 12

V and internal resistance 4.0 Ω. The potential difference across the filament of the lamp is 3.0 V and

the current in the filament is 0.25 A.

(i) Define emf and describe the concept of internal resistance.

emf:

...........................................................................................................................

...........................................................................................................................

Internal resistance:

...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the total power supplied by the battery.

...........................................................................................................................

........................................................................................................................... (1)


(iii) Calculate the power dissipated in the external circuit.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iv) Determine the resistance of the resistor R.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 16 marks)


(a) A heating coil is to be made of wire of diameter 3.5 × 10–4

m. The heater is to dissipate 980 W when

connected to a 230 V d.c. supply. The material of the wire has resistivity

1.3 × 10–6

Ω m at the working temperature of the heater.

(i) Define electrical resistance.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the resistance of the heating coil at its normal working temperature.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(iii) Show that the length of wire needed to make the heating coil is approximately 4 m.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) Three identical electrical heaters each provide power P when connected separately to a supply S which

has zero internal resistance. On the diagram below, complete the circuit by drawing two switches so

that the power provided by the heaters may be either P or 2P or 3P.

(2)

(Total 7 marks)

116. This question is about electric circuits

The components shown below are to be connected in a circuit to investigate how the current I in a tungsten

filament lamp varies with the potential difference V across it.


(a) Construct a circuit diagram to show how these components should be connected together in order to

obtain as large a range as possible for values of potential difference across the lamp.

(4)

(b) On the axes, sketch a graph of I against V for a filament lamp in the range V = 0 to its normal working

voltage.

(2)

(c) The lamp is marked with the symbols “1.25 V, 300 mW”. Calculate the current in the filament when it

is working normally.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)


(d) The resistivity of tungsten at the lamp’s working temperature is 4 × 10–7

Ωm. The total length of the

tungsten filament is 0.80 m. Estimate the radius of the filament.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(e) The cell is connected to two identical lamps connected in parallel. The lamps are rated at 1.25 V, 300

mW. The cell has an emf of 1.5 V and an internal resistance of 1.2 Ω.

Determine whether the lamps will light normally.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(Total 15 marks)


117. This question is about an electric circuit.

A particular filament lamp is rated at 12 V, 6.0 mA. It just lights when the potential difference across the

filament is 6.0 V.

A student sets up an electric circuit to measure the I-V characteristic of the filament lamp.

In the circuit, shown below, the student has connected the voltmeter and the ammeter into the circuit

incorrectly.

The battery has emf 12 V and negligible internal resistance. The ammeter has negligible resistance and the

resistance of the voltmeter is 100 k. The maximum resistance of the variable resistor is 15.

(a) Explain, without doing any calculations, whether there is a position of the slide S at which the lamp

will be lit.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (3)

(b) Estimate the maximum reading of the ammeter.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)


(c) Complete the circuit diagram below showing the correct position of the voltmeter and of the ammeter

in order to determine the I-V characteristic of the filament lamp.

(2)

(Total 7 marks)


118. This question is about simple harmonic motion and waves.

An object is vibrating in air. The variation with displacement x of the acceleration a of the object is shown

below.


(a) State and explain two reasons why the graph opposite indicates that the object is executing simple

harmonic motion.

1. ..................................................................................................................................

......................................................................................................................................

......................................................................................................................................

2. ..................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(b) Use data from the graph to show that the frequency of oscillation is 350 Hz.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(c) State the amplitude of the vibrations.

...................................................................................................................................... (1)

(d) The motion of the object gives rise to a longitudinal progressive (travelling) sound wave.

(i) State what is meant by a longitudinal progressive wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) The speed of the wave is 330 m s–1

. Using the answer in (b), calculate the wavelength of the

wave.

...........................................................................................................................

........................................................................................................................... (2)

(Total 13 marks)

119. This question is about simple harmonic motion.

(a) In terms of the acceleration, state two conditions necessary for a system to perform simple harmonic

motion.

1. ..................................................................................................................................

2. .................................................................................................................................. (2)

(b) A tuning fork is sounded and it is assumed that each tip vibrates with simple harmonic motion.

The extreme positions of the oscillating tip of one fork are separated by a distance d.

(i) State, in terms of d, the amplitude of vibration.

...........................................................................................................................

........................................................................................................................... (1)


(ii) On the axes below, sketch a graph to show how the displacement of one tip of the tuning fork

varies with time.

(1)

(iii) On your graph, label the time period T and the amplitude a. (2)

(c) The frequency of oscillation of the tips is 440 Hz and the amplitude of oscillation of each tip is 1.2

mm. Determine the maximum

(i) linear speed of a tip.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) acceleration of a tip.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 10 marks)


120. Simple harmonic motion and the greenhouse effect

(a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute

simple harmonic motion.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

......................................................................................................................... (2)

(b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be regarded as

two masses attached by a spring. A hydrogen atom is much less massive than the carbon atom such

that any displacement of the carbon atom may be ignored.

The graph below shows the variation with time t of the displacement x from its equilibrium position of

a hydrogen atom in a molecule of methane.

The mass of hydrogen atom is 1.7 10–27

kg. Use data from the graph above

(i) to determine its amplitude of oscillation.

......................................................................................................................... (1)


(ii) to show that the frequency of its oscillation is 9.1 1013

Hz.

.........................................................................................................................

......................................................................................................................... (2)

(iii) to show that the maximum kinetic energy of the hydrogen atom is 6.2 10–18

J.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) On the grid below, sketch a graph to show the variation with time t of the velocity v of the hydrogen

atom for one period of oscillation starting at t = 0. (There is no need to add values to the velocity axis.)

(3)


(d) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is

given by the expression

,2

1

pm

kf

where k is the force per unit displacement between a hydrogen atom and the carbon atom and mp is the

mass of a proton.

(i) Show that the value of k is approximately 560 N m–1

.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Estimate, using your answer to (d)(i), the maximum acceleration of the hydrogen atom.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(e) Methane is classified as a greenhouse gas.

(i) Describe what is meant by a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)


(ii) Electromagnetic radiation of frequency 9.1 1013

Hz is in the infrared region of the

electromagnetic spectrum. Suggest, based on the information given in (b)(ii), why methane is

classified as a greenhouse gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 17 marks)

121. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time,

the displacement of particles in the medium varies with position. Which arrow represents the direction of the

velocity of the particle marked P?

(Total 1 mark)


122. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Which graph shows how the object’s acceleration a varies with time t?

(Total 1 mark)


123. A particle oscillates with simple harmonic motion with period T.

At time t = 0, the particle has its maximum displacement. Which graph shows the variation with time t of the

kinetic energy Ek of the particle?

(Total 1 mark)

124. Two waves meet at a point. The waves have a path difference of 4

. The phase difference between the waves

is

A. 8

π rad.

B. 4

π rad.

C. 2

π rad.

D. π rad. (Total 1 mark)


125. The graph shows how the velocity v of an object undergoing simple harmonic motion varies with time t for

one complete period of oscillation.

Which of the following sketch graphs best shows how the total energy E of the object varies with t?

(Total 1 mark)


126. A force that varies sinusoidally is applied to a system that is lightly damped. Which of the following must be

true of the force for resonance to occur?

A. It must always be in anti-phase with the oscillations of the system.

B. Its direction must always be in the direction of motion of the oscillations of the system.

C. Its frequency must be equal to the frequency of oscillation of the system.

D. Its amplitude must be equal to the amplitude of oscillation of the system. (Total 1 mark)

127. Which of the following is a value of wavelength that is found in the visible region of the electromagnetic

spectrum?

A. 4 × 10–5

m

B. 4 × 10–7

m

C. 4 × 10–9

m

D. 4 × 10–11

m (Total 1 mark)

128. Two waves meet at a point in space. Which of the following properties always add together?

A. Displacement

B. Amplitude

C. Speed

D. Frequency (Total 1 mark)


129. The shock absorbers of a car, in good working condition, ensure that the vertical oscillations of the car are

A. undamped.

B. lightly damped.

C. moderately damped.

D. critically damped. (Total 1 mark)

130. The graphs show how the acceleration a of four different particles varies with their displacement x.

Which of the particles is executing simple harmonic motion?

(Total 1 mark)


131. The diagram below is a snapshot of wave fronts of circular waves emitted by a point source S at the surface

of water. The source vibrates at a frequency f = 10.0 Hz.

The speed of the wave front is

A. 0.15 cm s–1

.

B. 1.5 cm s–1

.

C. 15 cm s–1

.

D. 30 cm s–1

. (Total 1 mark)


132. Two coherent point sources S1 and S2 emit spherical waves.

Which of the following best describes the intensity of the waves at P and Q?

P Q

A. maximum minimum

B. minimum maximum

C. maximum maximum

D. minimum minimum

(Total 1 mark)


133. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the

variation with time t of the displacement x. The amplitude is x0 and the period of oscillation is T.

Which of the following is the correct expression for the displacement x?

A. tT

x2

cos0

B. tT

x2

cos0

C. tT

x2

sin0

D. tT

x2

sin0

(Total 1 mark)


134. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the

variation with time t of the displacement x. The amplitude is x0 and the period of oscillation is T.

Which of the following is the correct expression for the maximum acceleration of the object?

A. 0

2x

T

B. 02

2x

T

C. 02

24x

T

D. 0

24x

T

(Total 1 mark)


135. One end of a horizontal string is fixed to a wall. A transverse pulse moves along the string as shown.

Which of the following statements are correct for the reflected pulse compared to the forward pulse?

I. It moves more slowly.

II. It has less energy.

III. It is inverted.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III (Total 1 mark)

136. Monochromatic light travels from air into water. Which of the following describes the changes in wavelength

and speed?

Wavelength Speed

A. increases decreases

B. increases increases

C. decreases increases

D. decreases decreases

(Total 1 mark)


137. Which graph correctly shows how the acceleration, a of a particle undergoing SHM varies with its

displacement, x from its equilibrium position?

(Total 1 mark)


138. A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance A and

released. Its subsequent oscillations have total energy E and time period T.

An identical mass is attached to an identical spring. The maximum displacement is 2A. Assuming this spring

obeys Hooke’s law, which of the following gives the correct time period and total energy?

New time period New energy

A. T 4E

B. T 2E

C. T2 4E

D. T2 2E

(Total 1 mark)

139. In which of the following regions of the electromagnetic spectrum is radiation of wavelength 600 nm

located?

A. microwaves

B. radio waves

C. visible light

D. X-rays (Total 1 mark)


140. What is the best estimate for the refractive index of a medium in which light travels at a speed of 2.7 × 108 m

s–1

?

A. 0.9

B. 1.0

C. 1.1

D. 2.7 (Total 1 mark)

141. For a system executing simple harmonic motion, the restoring force acting on the system is proportional to

the

A. displacement of the system from equilibrium.

B. amplitude of oscillation.

C. elastic potential energy.

D. frequency of oscillation. (Total 1 mark)

142. A cart, connected to two identical springs, is oscillating with simple harmonic motion between two points X

and Y that are equidistant from point O.

The cart is in equilibrium at

A. all points between X and Y.

B. point O only.

C. points X and Y only.

D. points O, X and Y only. (Total 1 mark)


143. During one complete oscillation, the amplitude of a damped harmonic motion changes from 1.5 cm to 0.30

cm. The total energy at the end of the oscillation is E2 and the total energy at the beginning of the oscillation

is E1. The ratio 1

2

E

E is

A. 5

1.

B. 25

1.

C. 5.

D. 25. (Total 1 mark)


144. Plane wavefronts are incident on a boundary between two media labelled 1 and 2 in the diagram.

The diagram of the wavefronts is drawn to scale.

The ratio of the refractive index of medium 2 to that of medium 1 is

A. 0.50.

B. 0.67.

C. 1.5.

D. 2.0. (Total 1 mark)


145. A wave pulse is travelling to the right along a string.

Which of the following best represents the direction of the velocity of the point P?

A. ↑

B. ↓

C. →

D. ← (Total 1 mark)

146. A ray of light is incident on a boundary between glass and air.

Which of the following is the refractive index of glass?

A. 3

1

sin

sin

B. 4

1

sin

sin

C. 2

3

sin

sin

D. 1

4

sin

sin

(Total 1 mark)


147. The graph below shows how the displacement x of a particle undergoing simple harmonic motion varies with

time t. The motion is undamped.

Which of the following graphs correctly shows how the velocity v of the particle varies with t?

(Total 1 mark)


148. The graph below shows how the displacement x of a particle undergoing simple harmonic motion varies with

time t. The motion is undamped.

Which of the following graphs shows how the total energy E of the particle varies with time t?

(Total 1 mark)


149. An orchestra playing on boat X can be heard by tourists on boat Y, which is situated out of sight of boat X

around a headland.

The sound from X can be heard on Y due to

A. refraction.

B. reflection.

C. diffraction.

D. transmission. (Total 1 mark)


150. The graph below shows the variation with time t of the displacement x of a particle undergoing simple

harmonic motion.

Which graph correctly shows the variation with time t of the acceleration a of the particle?

(Total 1 mark)


151. A wooden block is at rest on a horizontal frictionless surface. A horizontal spring is attached between the

block and a rigid support.

The block is displaced to the right by an amount X and is then released. The period of oscillations is T and the

total energy of the system is E.

For an initial displacement of 2

X which of the following shows the best estimate for the period of

oscillations and the total energy of the system?

Period Total energy

A. T 2

E

B. T 4

E

C. 2

T

2

E

D. 2

T

4

E

(Total 1 mark)

152. Which of the following correctly describes the change, if any, in the speed, wavelength and frequency of a

light wave as it passes from air into glass?

Speed Wavelength Frequency

A. decreases decreases unchanged

B. decreases unchanged decreases

C. unchanged increases decreases

D. increases increases unchanged

(Total 1 mark)


153. The diagram below shows a pulse travelling along a rope from X to Y. The end Y of the rope is tied to a

fixed support.

When the pulse reaches end Y it will

A. disappear.

B. cause the end of the rope at Y to oscillate up and down.

C. be reflected and be inverted.

D. be reflected and not be inverted. (Total 1 mark)


154. The graph below shows the variation with time t of the displacement x of a particle undergoing simple

harmonic motion.

Which graph correctly shows the variation with time t of the acceleration a of the particle?

(Total 1 mark)

155. One electronvolt is equal to

A. 1.6 × 10–19

C.

B. 1.6 × 10–19

J.

C. 1.6 × 10–19

V.

D. 1.6 × 10–19

W. (Total 1 mark)


156. A point charge of magnitude 2.0 μC is moved between two points X and Y. Point X is at a potential of +6.0

V and point Y is at a potential of +9.0 V. The gain in potential energy of the point charge is

A. 0.20 μJ.

B. 1.5 μJ.

C. 6.0 μJ.

D. 30 μJ. (Total 1 mark)

157. A resistor of resistance 12 Ω is connected in series with a cell of negligible internal resistance. The power

dissipated in the resistor is P. The resistor is replaced with a resistor of resistance 3.0 Ω. What is the power

dissipated in this resistor?

A. 0.25 P

B. P

C. 2.0 P

D. 4.0 P (Total 1 mark)

158. The electromotive force (emf) of a cell is defined as

A. the power supplied by the cell per unit current from the cell.

B. the force that the cell provides to drive electrons round a circuit.

C. the energy supplied by the cell per unit current from the cell.

D. the potential difference across the terminals of the cell. (Total 1 mark)


159. A copper wire, of electric resistance R, has a length L and a cross-section area S. Another copper wire has a

length 2L and a cross-section area of 2

S. Which of the following is the resistance of this wire?

A. 4

R

B. 2

R

C. 2R

D. 4R (Total 1 mark)

160. The circuit shows a light-dependent resistor (LDR) in series with a resistor and a cell. The emf of the cell is ε.

The internal resistance of the cell is negligible.

When light shines on the LDR, the potential difference across the resistor will

A. stay the same.

B. decrease.

C. increase but always be less than ε.

D. increase and exceed ε. (Total 1 mark)


161. Two resistors, made of the same material, are connected in series to a battery. The length of resistor X is

twice that of resistor Y, and X has twice the cross-sectional area of Y.

Which of the following gives Y of resistance

X of resistance?

A. 4

1

B. 2

1

C. 1

D. 4 (Total 1 mark)

162. The circuit shows a resistor R connected in series with a battery and a resistor of resistance 10 Ω. The emf of

the battery is 20 V and it has negligible internal resistance. The current in the circuit is 1.0 A.

Which of the following is the resistance of R?

A. 1.0 Ω

B. 2.0 Ω

C. 10 Ω

D. 20 Ω (Total 1 mark)

163. Three identical resistors are connected to a battery as shown.


Which of the following is a correct statement?

A. The current through X is greater than that through Z.

B. The potential difference across Z is greater than that across Y.

C. The potential difference across resistor X and Y together is the same as that across Z.

D. The current through Z is less than the total current through X and Y. (Total 1 mark)

164. Two rectangular blocks, X and Y, of the same material have different dimensions but the same overall

resistance. Which of the following equations is correct?

A. resistivity of X × length of X = resistivity of Y × length of Y

B. Y

Y

X

X

of area sectional cross

oflength


oflength

C. resistivity of X × cross sectional area of X = resistivity of Y × cross sectional area of Y

D. X

Y

Y

X


oflength


oflength

(Total 1 mark)


165. Two 6 Ω resistors are connected in series with a 6 V cell. A student incorrectly connects an ammeter and a

voltmeter as shown below.

The readings on the ammeter and on the voltmeter are

Ammeter reading / A Voltmeter reading / V

A. 0.0 0.0

B. 0.0 6.0

C. 1.0 0.0

D. 1.0 6.0

(Total 1 mark)


166. The diagram shows a potential divider circuit.

In order to increase the reading on the voltmeter the

A. temperature of R should be increased.

B. temperature of R should be decreased.

C. light intensity on R should be increased.

D. light intensity on R should be decreased. (Total 1 mark)


167. The tungsten filament of a lamp has a cross-sectional area A and length L. For a potential difference V across

the filament, the current in the filament is I. The resistivity of the tungsten equals

A. LI

AV.

B. AV

LI.

C. AI

LV.

D. LV

AI

(Total 1 mark)

168. Which of the following is a correct unit of electromotive force (emf)?

A. A Ω–1

B. Ω A–1

C. C J–1

D. J C–1

(Total 1 mark)

169. Which of the following correctly gives the resistance of an ideal ammeter and resistance of an ideal

voltmeter?

Ammeter Voltmeter

A. infinite infinite

B. zero zero

C. zero infinite

D. infinite zero

(Total 1 mark)


170. A cell of emf ε and internal resistance r delivers current to a small electric motor.

450 C of charge flows through the motor and 9000 J of energy are converted in the motor. 1800 J are

dissipated in the cell. The emf of the cell is

A. 4.0 V.

B. 16 V.

C. 20 V.

D. 24 V. (Total 1 mark)

171. A cylindrical conductor of length l, diameter D and resistivity ρ has resistance R. A different cylindrical

conductor of resistivity 2 ρ, length 2l and diameter 2D has a resistance

A. 2R.

B. R.

C. 2

R.

D. 4

R.

(Total 1 mark)


172. In the circuits below the cells have the same emf and zero internal resistance. The resistors all have the same

resistance.

Which of the following gives the ratio Yin dissipatedpower

Xin dissipatedpower ?

A. 4

1

B. 2

1

C. 2

D. 4 (Total 1 mark)


173. In the circuit below, the battery has negligible internal resistance. Three identical lamps L, M and N of

constant resistance are connected as shown.

The filament of lamp N breaks. Which of the following shows the subsequent changes to the brightness of

lamp L and lamp M?

Lamp L Lamp M

A. stays the same decreases

B. increases stays the same

C. increases decreases

D. decreases increases

(Total 1 mark)

174. An electron passes the north pole of a bar magnet as shown below.

What is the direction of the magnetic force on the electron?

A. Into the page

B. Out of the page

C. To the left

D. To the right (Total 1 mark)


175. The definition of the ampere refers to the

A. number of electrons passing a given point per second.

B. force between parallel current-carrying conductors.

C. power dissipated per unit resistance.

D. amount of charge transferred per second. (Total 1 mark)

176. Two isolated point charges, –7 μC and +2 μC, are at a fixed distance apart. At which point is it possible for

the electric field strength to be zero?

(not to scale)

(Total 1 mark)

177. The weight of an object of mass 1 kg at the surface of Mars is about 4 N. The radius of Mars is about half the

radius of Earth. Which of the following is the best estimate of the ratio below?

Earth of mass

Mars of mass

A. 0.1

B. 0.2

C. 5

D. 10 (Total 1 mark)


178. Three positive point charges of equal magnitude are held at the corners X, Y and Z of a right-angled triangle.

The point P is at the midpoint of XY. Which of the arrows shows the direction of the electric field at point P?

(Total 1 mark)


179. An electron travelling in the direction shown by the arrow X, enters a region of uniform magnetic field. It

leaves the region of field in the direction shown by the arrow Y.

The direction of the magnetic field is

A. in the direction of X.

B. into the plane of the paper.

C. in the opposite direction to X.

D. out of the plane of the paper. (Total 1 mark)


180. The radius of a charged spherical conductor is R. Which of the following graphs best shows how the

magnitude of the electrical field strength E varies with distance r from the centre of the sphere?

(Total 1 mark)

181. Which of the following gives the acceleration of an electron of electric charge e and mass m in a uniform

electric field of strength E?

A. E

B. Ee

C. m

Ee

D. Ee

m

(Total 1 mark)


182. A particle, of mass m and charge q, moves with velocity v perpendicularly to a magnetic field. The

magnitude of the magnetic force acting on the particle at a particular point is F. Which of the following gives

the magnitude of the magnetic field strength at that point?

A. q

F

B. m

F

C.

F

D. q

F

(Total 1 mark)

183. A current is established in a coil of wire in the direction shown.

The direction of the magnetic field at point P is

A. out of the plane of the paper.

B. into the plane of the paper.

C. to the left.

D. to the right. (Total 1 mark)


184. Which arrangement of three point charges at the corner of an equilateral triangle will result in a zero electric

field strength at the centre of the triangle, point P?

(Total 1 mark)

185. The mass of a planet is twice that of Earth. Its radius is half that of the radius of Earth. The gravitational field

strength at the surface of Earth is g. The gravitational field strength at the surface of the planet is

A. g2

1.

B. g.

C. 2g.

D. 8g. (Total 1 mark)


186. An electron enters the vacuum between two oppositely charged plates with velocity v. The electron is

followed by an alpha particle moving with the same initial velocity as the electron. A uniform magnetic field

is directed out of the plane of the paper.

The electron’s path is undeflected. The path of the alpha particle will be

A. deflected out of the plane of the paper.

B. undeflected.

C. deflected upward.

D. deflected downward. (Total 1 mark)

187. The mass of Earth is ME, its radius is RE and the magnitude of the gravitational field strength at the surface of

Earth is g. The universal gravitational constant is G. The ratio G

g is equal to

A. 2E

E

R

M

B. E

2E

M

R

C. MERE

D. 1 (Total 1 mark)


188. Which diagram best represents the electric field due to a negatively charged conducting sphere?

(Total 1 mark)


189. A point mass carries a positive charge +Q and is at rest in a magnetic field. The field is in the direction

shown.

The magnetic force acting on the charge is

A. from left to right in the plane of the page.

B. from top to bottom in the plane of the page.

C. into the plane of the page.

D. zero. (Total 1 mark)

190. The gravitational force between two unit masses separated by a distance r is Fg. The electric force between

two unit charges separated by a distance r is Fe. The Coulomb constant is k and the universal gravitational

constant is G. The ratio Fg / Fe is

A. one.

B. G

k.

C. k

G.

D. Gk. (Total 1 mark)


191. A hollow metallic sphere is negatively charged. Which of the following correctly represents the electric

field?

(Total 1 mark)

192. In the diagram, a long current-carrying wire is normal to the plane of the paper. The current in the wire is

directed into the plane of the paper.

Which of the arrows gives the direction of the magnetic field at point P?

A. W

B. X

C. Y

D. Z (Total 1 mark)


193. A small sphere X of mass M is placed a distance d from a point mass. The gravitational force on sphere X is

90 N. Sphere X is removed and a second sphere Y of mass 4M is placed a distance 3d from the same point

mass. The gravitational force on sphere Y is

A. 480 N.

B. 160 N.

C. 120 N.


194. Which of the following diagrams illustrates the electric field pattern of a negatively charged sphere?

(Total 1 mark)


195. A positively charged particle enters the space between two charged conducting plates, with a constant

velocity directed parallel to the plates, as shown.

The top plate is positively charged and the bottom plate is negatively charged. There is a magnetic field in the

shaded region PQRS. The particle continues to move in a horizontal straight line between the plates. Which

of the following correctly describes the magnetic field direction?

A. Into plane of paper

B. Out of plane of paper

C. Up

D. Down (Total 1 mark)

196. In Newton’s universal law of gravitation the masses are assumed to be

A. extended masses.

B. masses of planets.

C. point masses.

D. spherical masses. (Total 1 mark)


197. The electric field strength at a point may be defined as

A. the force exerted on unit positive charge placed at that point.

B. the force per unit positive charge on a small test charge placed at that point.

C. the work done on unit positive charge to move the charge to that point from infinity.

D. the work done per unit positive charge to move a small test charge to that point from infinity. (Total 1 mark)

198. An electron is moving in air at right angles to a uniform magnetic field. The diagram below shows the path of

the electron. The electron is slowing down.

Which of the following correctly gives the direction of motion of the electron and the direction of the

magnetic field?

Direction of motion Direction of magnetic field

A. clockwise into plane of paper

B. clockwise out of plane of paper

C. anti-clockwise into plane of paper

D. anti-clockwise out of plane of paper

(Total 1 mark)


199. In the circuit below, the voltmeter has a resistance 100 k. The battery has negligible internal resistance and

emf 6 V.

The reading on the voltmeter is

A. 0 V.

B. 2 V.

C. 3 V.

D. 4 V. (Total 1 mark)


200. In the circuit shown below, the cell has negligible internal resistance.

Which of the following equations is correct?

A. I1 = 2I2

B. I1 = 2I3

C. I2 = 2I3

D. I3 = 2I1

(Total 1 mark)

201. A spherical planet of uniform density has three times the mass of the Earth and twice the average radius. The

magnitude of the gravitational field strength at the surface of the Earth is g.

What is the gravitational field strength at the surface of the planet?

A. 6 g

B. g3

2

C. g4

3

D. g2

3

(Total 1 mark)


202. A spacecraft travels away from Earth in a straight line with its motors shut down. At one instant the speed of

the spacecraft is 5.4 km s–1

. After a time of 600 s, the speed is 5.1 km s–1

. The average gravitational field

strength acting on the spacecraft during this time interval is

A. 5.0 × 10–4

N kg–1

B. 3.0 × 10–2

N kg–1

C. 5.0 × 10–1

N kg–1

D. 30 N kg–1

(Total 1 mark)

203. A long straight wire carries an electric current perpendicularly out of the paper. Which of the following

represents the magnetic field pattern due to the current?

(Total 1 mark)


204. This question is about electric charge.

(a) A plastic rod XY is held at end X. The end Y is rubbed with a piece of cloth and, as a result, the end Y

becomes electrically charged.

The procedure is now repeated using a copper rod and it is found that the copper rod remains

electrically neutral. Explain these observations in terms of the properties of conductors and insulators.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (5)


(b) Two plastic rods each have a positive charge +q situated at one end. The rods are arranged as shown.

Assume that the charge at the end of each rod behaves as a point charge. Draw, in the shaded area on

the diagram, the electric field pattern due to the two charges. (2)

(Total 7 marks)

205. This question is about electric and gravitational fields

(a) State, in terms of electrons, the difference between a conductor and an insulator.

......................................................................................................................................

...................................................................................................................................... (1)


(b) Suggest why there must be an electric field inside a current-carrying conductor.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c) The magnitude of the electric field strength inside a conductor is 55 N C–1

. Calculate the force on a

free electron in the conductor.

......................................................................................................................................

...................................................................................................................................... (1)

(d) The electric force between two point charges is a fundamental force as is the gravitational force

between two point masses. State one similarity between these two forces and one difference (other

than the fact that one applies to charge and the other to mass).

Similarity: ...................................................................................................................

......................................................................................................................................

Difference: ..................................................................................................................

...................................................................................................................................... (2)

(e) The force on a mass of 1.0 kg falling freely near the surface of Jupiter is 25 N. The radius of Jupiter is

7.0 × 107 m.

(i) State the value of the magnitude of the gravitational field strength at the surface of Jupiter.

........................................................................................................................... (1)


(ii) Calculate that the mass of Jupiter is about 1.8 × 1027

kg.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 10 marks)

206. This question is about a lightning discharge.

(a) Define electric field strength.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) A thundercloud can be modelled as a negatively charged plate that is parallel to the ground.

The magnitude of the charge on the plate increases due to processes in the atmosphere. Eventually a

current discharges from the thundercloud to the ground.

On the diagram, draw the electric field pattern between the thundercloud base and the ground. (3)


(c) The magnitude of the electric field strength E between two infinite charged parallel plates is given by

the expression

E = 0

where σ is the charge per unit area on one of the plates.

A thundercloud carries a charge of magnitude 35 C spread over its base. The area of the base is 1.2 ×

107 m

2.

(i) Determine the magnitude of the electric field between the base of the thundercloud and the

ground.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) State two assumptions made in (c)(i).

1. .......................................................................................................................

...........................................................................................................................

2. .......................................................................................................................

........................................................................................................................... (2)


(iii) When the thundercloud discharges, the average discharge current is 1.8 kA. Estimate the

discharge time.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iv) The potential difference between the thundercloud and the ground before discharge is 2.5 × 108

V. Determine the energy released in the discharge.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 17 marks)

207. This question is about force fields.

(a) Outline what is meant by a field of force.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) Five particles A to E are each placed in a different type of field. Complete the table to identify the

nature of the field in which each particle is situated.

Particle Charge on

particle

Initial direction of

motion of particle

Direction of

force on particle Type of field

A uncharged stationary in direction of

field .....................................

B negative along direction of

field

opposite to

direction of field .....................................

C positive normal to direction

of field

normal to

direction of field .....................................

D positive normal to direction

of field

in direction of

field .....................................

E uncharged opposite to direction

of field

in direction of

field .....................................

(5)

(Total 7 marks)

208. This question is about gravitational and electric fields.

(a) The equation for the magnitude of the gravitational field strength due to a point mass may be written as

below.

Y = 2s

KX

The equation for the magnitude of the electric field strength can also be written in the same form.

In the table identify the symbols used in the equation.

Symbol Gravitational field quantity Electrical field quantity

Y

K

X

s

(4)


(b) The magnitude of the electrostatic force between the proton and electron in a hydrogen atom is FE. The

magnitude of the gravitational force between them is FG.

Determine the ratio G

E

F

F.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 7 marks)

209. This question is about gravitational fields.

(a) Define gravitational field strength.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)


(b) The gravitational field strength at the surface of Jupiter is 25 N kg–1

and the radius of Jupiter is 7.1

107 m.

(i) Derive an expression for the gravitational field strength at the surface of a planet in terms of its

mass M, its radius R and the gravitational constant G.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) Use your expression in (b)(i) above to estimate the mass of Jupiter.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 6 marks)

210. A freshly prepared sample contains 4.0 μg of iodine-131. After 24 days, 0.5 μg of iodine-131 remain. The

best estimate of the half-life of iodine-131 is

A. 8 days.

B. 12 days.

C. 24 days.

D. 72 days. (Total 1 mark)


211. This question is about nuclear physics.

(a) (i) Define binding energy of a nucleus.

...........................................................................................................................

........................................................................................................................... (1)

(ii) The mass of a nucleus of plutonium ( Pu23994 ) is 238.990396 u. Deduce that the binding energy

per nucleon for plutonium is 7.6 MeV.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(b) The graph shows the variation with nucleon number A of the binding energy per nucleon.

Plutonium ( Pu23994 ) undergoes nuclear fission according to the reaction given below.

n BaSr n Pu 10

14656

9138

10

23994 x

(i) Calculate the number x of neutrons produced.

........................................................................................................................... (1)

(ii) Use the graph to estimate the energy released in this reaction.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(c) Stable nuclei with a mass number greater than about 20, contain more neutrons than protons. By

reference to the properties of the nuclear force and of the electrostatic force, suggest an explanation for

this observation.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(Total 11 marks)


212. This question is about the photoelectric effect.

In an experiment to investigate the photoelectric effect, light of frequency f is incident on the metal surface

A, shown in the diagram below. A potential difference is applied between A and B. The photoelectric current

is measured by a sensitive ammeter. (Note: the complete electrical circuit is not shown.)

When the frequency of the light is reduced to a certain value, the current measured by the ammeter becomes

zero. Explain how Einstein’s photoelectric theory accounts for this observation.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................ (Total 4 marks)


213. This question is about atomic spectra.

Diagram 1 shows some of the energy levels of the hydrogen atom. Diagram 2 is a representation of part of

the emission spectrum of atomic hydrogen. The lines shown represent transitions involving the –3.40 eV

level.

(a) Deduce that the energy of a photon of wavelength 658 nm is 1.89 eV.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) (i) On diagram 1, draw an arrow to show the electron transition between energy levels that gives

rise to the emission of a photon of wavelength 658 nm. Label this arrow with the letter A. (1)


(ii) On diagram 1, draw arrows to show the electron transitions between energy levels that give rise

to the emission of photons of wavelengths 488 nm, 435 nm and 411 nm.

Label these arrows with the letters B, C and D. (1)

(c) Explain why the lines in the emission spectrum of atomic hydrogen, shown in diagram 2, become

closer together as the wavelength of the emitted photons decreases.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 8 marks)

214. This question is about radioactive decay.

Iodine-124 (I-124) is an unstable radioisotope with proton number 53. It undergoes beta plus decay to form

an isotope of tellurium (Te).

(a) State the reaction for the decay of the I-124 nuclide.

...................................................................................................................................... (2)


(b) The graph below shows how the activity of a sample of iodine-124 changes with time.

(i) State the half-life of iodine-124

........................................................................................................................... (1)

(ii) Calculate the activity of the sample at 21 days.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(iii) A sample of an unknown radioisotope has a half-life twice that of iodine-124 and the same

initial activity as the sample of iodine-124. On the axes opposite, draw a graph to show how the

activity of the sample would change with time.

Label this graph X. (1)

(iv) A second sample of iodine-124 has half the initial activity as the original sample of iodine-124.

On the axes opposite, draw a graph to show how the activity of this sample would change with

time. Label this graph Y. (1)

(Total 8 marks)

215. Which nucleons in a nucleus are involved in the Coulomb interaction and the strong short-range nuclear

interaction?

Coulomb interaction Strong short-range interaction

A. protons protons, neutrons

B. protons neutrons

C. protons protons

D. protons, neutrons neutrons

(Total 1 mark)


216. Two samples of radioactive substances X and Y have the same initial activity. The half-life of X is T and the

half-life of Y is 3T. After a time of 3T the ratio

Y substance ofactivity

X substance ofactivity is

A. 8.

B. 4.

C. 4

1.

D. 8

1.

(Total 1 mark)

217. The nuclear equation below is an example of the transmutation of mercury into gold.

Au Hg H 19779

19980

21 + X

The particle X is a

A. gamma-ray photon.

B. helium nucleus.

C. proton.

D. neutron. (Total 1 mark)

218. This question is about unified atomic mass unit and a nuclear reaction.

(a) Define the term unified atomic mass unit.

......................................................................................................................................

...................................................................................................................................... (1)


(b) The mass of a nucleus of rutherfordium-254 is 254.1001 u. Calculate the mass in GeV c–2

.

......................................................................................................................................

...................................................................................................................................... (1)

(c) In 1919, Rutherford produced the first artificial nuclear transmutation by bombarding nitrogen with

α-particles. The reaction is represented by the following equation.

α + O N 178

147 + X

(i) Identify X.

........................................................................................................................... (1)

(ii) The following data are available for the reaction.

Rest mass of α = 3.7428 GeV c–2

Rest mass of N147 = 13.0942 GeV c

–2

Rest mass of O178 + X = 16.8383 GeV c

–2

The initial kinetic energy of the α-particle is 7.68 MeV. Determine the sum of the kinetic

energies of the oxygen nucleus and X. (Assume that the nitrogen nucleus is stationary.)

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(d) The reaction in (c) produces oxygen (O-17). Other isotopes of oxygen include O-19 which is

radioactive with a half-life of 30 s.

(i) State what is meant by the term isotopes.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Define the term radioactive half-life.

...........................................................................................................................

........................................................................................................................... (1)

(e) A nucleus of the isotope O-19 decays to a stable nucleus of fluorine. The half-life of O-19 is 30 s. At

time t = 0, a sample of O-19 contains a large number N0 nuclei of O-19.

On the grid below, draw a graph to show the variation with time t of the number N of O-19 nuclei

remaining in the sample. You should consider a time of t = 0 to t = 120 s.

(2)

(Total 10 marks)



(a) State what is meant by the photoelectric effect.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(b) Light of frequency 8.7 × 1014

Hz is incident on the surface of a metal in a photocell.

The surface area of the metal is 9.0 × 10–6

m2 and the intensity of the light is

1.1 × 10–3

W m–2

.

(i) Deduce that the maximum possible photoelectric current in the photocell is 2.7 nA.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) The maximum kinetic energy of photoelectrons released from the metal surface is 1.2 eV.

Calculate the value of the work function of the metal.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(Total 5 marks)


220. This question is about the de Broglie hypothesis.

(a) State the de Broglie hypothesis.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Determine the de Broglie wavelength of a proton that has been accelerated from rest through a

potential difference of 1.2 kV.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) Explain why a precise knowledge of the de Broglie wavelength of the proton implies that its position

cannot be observed.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 6 marks)



Nitrogen-13 ( N137 ) is an isotope that is used in medical diagnosis. The decay constant of nitrogen-13 is 1.2 ×

10–3

s–1

.

(a) (i) Define decay constant.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(ii) A sample of nitrogen-13 has an initial activity of 800 Bq. The sample cannot be used for

diagnostic purposes if its activity becomes less than 150 Bq. Determine the time it takes for the

activity of the sample to fall to 150 Bq.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) (i) Calculate the half-life of nitrogen-13

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)


(ii) Outline how the half-life of a sample of nitrogen-13 can be measured in a laboratory.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Nitrogen-13 undergoes β+ decay. Outline the experimental evidence that suggests another particle, the

neutrino, is also emitted in the decay.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 9 marks)


222. This question is about nuclear processes.

(a) A nucleus of radium-91 ( Ra22691 ) undergoes alpha particle decay to form a nucleus of radon (Rn).

(i) Identify the proton number and nucleon number of the nucleus of Rn.

Proton number: .................................................................................................

Nucleon number: .............................................................................................. (2)

(ii) The half-life of radium-91 is 1600 years. Determine the length of time taken for 87.5 % of the

radium to disintegrate.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) Immediately after the decay of a stationary radium nucleus, the alpha particle and the radon nucleus

move off in opposite directions and at different speeds.

Outline the reasons for these observations.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)


(c) Outline why a beta particle has a longer range in air than an alpha particle of the same energy.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 10 marks)

223. This question is about the wave nature of matter.

(a) Describe the de Broglie hypothesis.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) Outline an experiment to verify the de Broglie hypothesis.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c) Show that the de Broglie wavelength of electrons accelerated from rest through a potential difference

of 150 V is 1.0 ×10–10

m.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 8 marks)


224. This question is about alpha (α) particle scattering.

An experiment is carried out in which alpha (α) particles of initial kinetic energy 5.0 MeV are fired at a piece

of gold foil. The proton number of gold is 79.

Determine the distance of closest approach of an alpha (α) particle to a gold nucleus.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................ (Total 4 marks)

225. This question is about β+ (positron) decay.

(a) In a β+ decay, a positron is emitted along with a neutrino, and a γ-ray photon.

Although the energy spectrum for γ-rays involved is discrete, the energy spectrum for the positrons is

continuous.

(i) State the difference between a discrete energy spectrum and a continuous energy spectrum.

...........................................................................................................................

........................................................................................................................... (1)


(ii) Explain how the existence of the neutrino accounts for the continuous nature of the positron

energy spectrum.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) Sodium-22 is a radioisotope used in nuclear medicine that undergoes β+ decay.

The half-life of sodium-22 is 2.6 years.

A sample of sodium-22 has an initial activity of 6.2 × 109 Bq.

(i) Define decay constant.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the decay constant of sodium-22.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)


(iii) Calculate the activity of the sample of sodium-22 after 8.0 years.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 8 marks)

226. This question is about fundamental interactions.

(a) State an exchange particle for

(i) the weak interaction.

........................................................................................................................... (1)

(ii) the electromagnetic interaction.

........................................................................................................................... (1)

(b) Comment, with reference to the mass of the exchange particles, on the range of the weak and

electromagnetic interactions.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(c) Describe the process represented by the Feynman diagram below.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(d) State what is meant by a virtual particle.

......................................................................................................................................

...................................................................................................................................... (1)

(e) Explain how the Heisenberg uncertainty principle for energy and time applies to the interaction in (c).

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(f) The uncertainty in the time for the electromagnetic interaction between two electrons is 1.6 × 10–16

s.

Determine the uncertainty in the energy of the virtual photon.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 10 marks)

227. This question is about radioactive decay and binding energy.

(a) Describe what is meant by radioactive decay.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) A nucleus of thallium-206 (Tl-206) undergoes radioactive decay to a nucleus of lead-206 (Pb-206). In

the reaction equation below, identify the proton number Z of lead and the particle x.

x Pb T 206Z

20682

Z: .................................................................................................................................

x: ................................................................................................................................. (2)


(c) The mass of a Tl-206 nucleus is 191 870 MeV c–2

. Determine the binding energy per nucleon of

Tl-206.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(d) State why the binding energy of Pb-206 is greater than that of Tl-206.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(Total 9 marks)


(a) In the photoelectric effect, electrons are emitted from a metal surface almost immediately after light is

incident on the surface, i.e. without any time delay. Explain this observation with reference to

Einstein’s theory of the photoelectric effect.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) The graph shows the variation with incident light frequency f of the maximum kinetic energy EK of the

emitted electrons.

Use the graph to

(i) estimate the work function of the metal surface.

...........................................................................................................................

........................................................................................................................... (1)

(ii) calculate the maximum speed of the emitted electrons for incident light of frequency 5.0 × 1015

Hz.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 6 marks)


229. This question is about quantum aspects of the electron.

(a) The energy of electrons in atoms is said to be quantized. State what is meant by quantized energy.

......................................................................................................................................

...................................................................................................................................... (1)

(b) An electron that is confined to move in a region of length L can only have energies given by the

equation

En = 2

22

π8 mL

nh

where n is a positive integer.

For L = 1.0 × 10–10

m, use the equation above to

(i) calculate that the smallest difference between the allowed energies of the electron is 5.8 × 10–18

J.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) determine the wavelength of the photon whose energy is 5.8 × 10–18

J.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(c) Part of the emission spectrum of hydrogen is shown in the diagram.

Suggest whether this spectrum can be explained by the model in (b).

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 8 marks)


(a) The decay constant for a particular isotope is λ = 0.048 s–1

. A sample of the isotope initially contains

2.0 × 1012

nuclei of this isotope.

(i) Define decay constant.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Estimate the number of nuclei that will decay in the first second.

...........................................................................................................................

........................................................................................................................... (1)


(b) The graph shows the variation with time t of the activity A of a sample containing radioactive material

that consists of two different isotopes. Each isotope decays into a stable daughter isotope.

(i) Use the graph to explain how it may be deduced that the sample contains more than one isotope.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) One of the isotopes in the sample has a half-life that is shorter than 0.20 s. Use the graph to

estimate the half-life of the other isotope. Explain your working.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 6 marks)


231. This question is about the Rutherford model of the atom.

(a) Most alpha particles used to bombard a thin gold foil pass through the foil without a significant change

in direction. A few alpha particles are deviated from their original direction through angles greater than

90°. Use these observations to describe the Rutherford atomic model.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (5)


(b) The isotope gold-197 ( Au19779 ) is stable but the isotope gold-199 ( Au199

79 ) is not.

(i) Outline, in terms of the forces acting between nucleons, why, for large stable nuclei such as

gold-197, the number of neutrons exceeds the number of protons.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) A nucleus of Au19979 decays to a nucleus of Hg199

80 with the emission of an electron and another

particle. State the name of this other particle.

...........................................................................................................................

........................................................................................................................... (1)

(Total 9 marks)


232. This question is about wave–particle duality.

(a) In the photoelectric effect, electrons are not emitted from the surface of a metal if the frequency of the

incident light is below a certain value called the threshold frequency.

(i) Explain, with reference to the Einstein model of the photoelectric effect, the existence of the

threshold frequency.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(ii) State, with reference to your answer in (a)(i), the reason why the threshold frequency is different

for different metals.

...........................................................................................................................

........................................................................................................................... (1)

(b) Light of frequency 1.0 × 1015

Hz is incident on the surface of a metal. The work function of the metal

is 3.2 × 10–19

J.

(i) Show that the maximum kinetic energy of the emitted electrons is 3.4 × 10–19

J.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) Determine the de Broglie wavelength of the electrons in (b)(i).

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 10 marks)


233. This question is about the spectrum of atomic hydrogen.

(a) The diagram represents the principal lines in the visible spectrum of atomic hydrogen.

Outline how the spectrum can be produced and observed in the laboratory.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)


(b) Calculate the difference in energy in eV between the energy levels in the hydrogen atom that give rise

to the red line in the spectrum.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)


(a) A nucleus of a radioactive isotope of gold (Au-189) emits a neutrino in the decay to a nucleus of an

isotope of platinum (Pt).

In the nuclear reaction equation below, state the name of the particle X and identify the nucleon

number A and proton number Z of the nucleus of the isotope of platinum.

vXAZ Pt Au189

79

X: ................................................................................................................................

A: ................................................................................................................................

Z: ................................................................................................................................ (2)

(b) The half-life of Au-189 is 8.84 minutes. A freshly prepared sample of the isotope has an activity of

124 Bq.

(i) Calculate the decay constant of Au-189.

...........................................................................................................................

........................................................................................................................... (1)


(ii) Determine the activity of the sample after 12.0 min.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 5 marks)

235. This question is about decay of radium-226.

(a) A nucleus of the isotope radium-226 (Ra) undergoes α-decay with a half-life of

1.6 × 103 yr to form a nucleus of radon (Rn).

Define the terms isotope and half-life.

Isotope: ........................................................................................................................

......................................................................................................................................

Half-life: ......................................................................................................................

...................................................................................................................................... (2)


(b) Using the grid below, sketch a graph to show how the activity A of a sample of radium-226 (Ra) would

be expected to vary with time t over a period of about 5.0 × 103 yr.

The activity of the sample at time t = 0 is A0.

(3)

(c) The nuclear reaction equation for the decay of radium-226 (Ra) may be written as

αRnRa22688

(i) State the value of the proton number and neutron number of the isotope of radon (Rn).

Proton number: .................................................................................................

Neutron number: ............................................................................................... (1)


(ii) Outline why the binding energy of Ra is less than that of Rn.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(d) The following data are available.

mass of Ra = 226.0254 u

mass of Rn = 222.0175 u

mass of α = 4.0026 u

Show that the energy released in the decay of a Ra nucleus is 4.94 MeV.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 10 marks)



(a) In the photoelectric effect, electrons are emitted from a metallic surface only if the wavelength of the

light incident on the surface is below a certain value called the threshold wavelength.

Explain this observation.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) A monochromatic source of power 3.0 W emits light of wavelength 4.60 × 10–7

m. All of the light is

incident on a metal surface and causes electrons to be emitted at a rate of

4.0 × 1010

s–1

. The threshold wavelength of the metal is 5.50 × 10–7

m.

Calculate the

(i) photoelectric current.

...........................................................................................................................

........................................................................................................................... (1)

(ii) work function of the metal.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(iii) the ratio of the rate of electron emission to the rate at which the photons are incident on the

metal.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Light from a different source is incident on the metal in (b). The new source has power 6.0 W and

emits light of wavelength 9.00 × 10–7

m.

State the effect of these changes, if any, on your answer to (b)(i).

......................................................................................................................................

...................................................................................................................................... (1)

(Total 10 marks)


237. This question is about quantum aspects of the electron.

The graph shows the variation with distance x of the wavefunction Ψ of an electron at a particular instant of

time. The electron is confined within a region of length 2.0 × 10–10

m.

(a) State what is meant by the wavefunction of an electron.

......................................................................................................................................

...................................................................................................................................... (1)

(b) Using data from the graph estimate, for this electron,

(i) its momentum.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) the uncertainty in its momentum.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 5 marks)

238. This question is about nuclear energy levels and radioactive decay.

The diagram shows some of the nuclear energy levels of the boron isotope B125 and the carbon isotope C12

6 .

Differences in energy between the levels are indicated on the diagram. A particular beta decay of boron and a

gamma decay of carbon are marked on the diagram.

(a) Calculate the wavelength of the photon emitted in the gamma decay.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(b) Calculate the maximum kinetic energy of the electron emitted in the beta decay indicated.

......................................................................................................................................

...................................................................................................................................... (1)

(c) Explain why the electrons emitted in the indicated beta decay of boron do not always have the kinetic

energy calculated in (b).

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

239. This question is about α-particle scattering and nuclear processes.

α-particle scattering

Radium-226 decays with the emission of α-particles to radon (Rn).

(a) Complete the nuclear reaction equation.

Ra22688 Rn +

(2)

(b) Experimental evidence that supports a nuclear model of the atom was provided by α-particle

scattering. The diagram represents the path of an α-particle as it approaches and then recedes from a

stationary gold nucleus.


(i) On the diagram, draw lines to show the angle of deviation of the α-particle.

Label this angle D. (1)

(ii) The gold nucleus is replaced by another gold nucleus that has a larger nucleon number. Suggest

and explain the change, if any, in the angle D of an α-particle with the same energy and

following the same initial path as in (b)(i).

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) The diagram shows the initial path of an α-particle that approaches the gold nucleus along a line

joining their centres. On the diagram draw the subsequent path of the α-particle.

(1)

Nuclear processes

(d) The main nuclear process that gives rise to energy emission from the Sun may be simplified to

4H → He + energy.

(i) State the name of this nuclear process.

........................................................................................................................... (1)


(ii) The total mass of four hydrogen (H) nuclei is 6.693 × 10–27

kg and the mass of a helium (He)

nucleus is 6.645 × 10–27

kg. Show that the energy released in this reaction is 4.3 × 10–12

J.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) The Sun has a radius R of 7.0 × 108 m and emits energy at a rate of 3.9 × 10

26 W.

The nuclear reactions take place in the spherical core of the Sun of radius 0.25R. Use these data

and the answer in (d)(ii) to determine the number of nuclear reactions occurring per cubic metre

per second in the core of the Sun.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 12 marks)


(a) A clean metal surface in a vacuum is illuminated with monochromatic light, resulting in the emission

of electrons from the surface.


(i) On the axes, sketch a graph to show how the maximum kinetic energy K of the electron varies

with the intensity I of the light.

(1)

(ii) Explain the shape of the graph you have drawn.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(b) The wavelength of the incident light in (a) is 400 nm. The maximum kinetic energy of the emitted

electrons is 2.1 eV. Determine the work function of the metal.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 7 marks)


241. This question is about the wave nature of matter and quantum energy states.

(a) Describe what is meant by the de Broglie hypothesis.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) An electron is confined to one dimension in a “box” of length L. The de Broglie waves associated with

the particle form standing waves in the box with wavelengths given by n

L2 where n is = 1, 2, 3, etc.

Show that the energy levels En for the particle are given by En = )8( 2

22

mL

hn where h is Planck’s

constant.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c) The electron makes a transition from the energy state given by n = 4 to n = 2. The length L = 1.3 ×

10–9

m. Calculate the

(i) energy of the photon emitted.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(ii) wavelength of the photon emitted.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 9 marks)

242. This question is about nuclear physics and radioactive decay.

(a) Define the decay constant of a radioactive nuclide.

......................................................................................................................................

...................................................................................................................................... (1)

(b) (i) Plutonium-239 (Pu-239) has a half-life of 2.4 × 104 years. Show that the decay constant of

Pu-239 is approximately 3 × 10–5

year–1

.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the time taken for the activity of a freshly-prepared sample of Pu-239 to fall to 0.1 %

of its initial value.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 4 marks)


243. This question is about nuclear fission and fusion.

(a) The graph shows the variation of binding energy per nucleon for nuclides with a nucleon number

greater than 40.

(i) Define binding energy.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(ii) On the graph, label with the letter S the position of the most stable nuclide. (1)

(iii) State why the nuclide you have labelled is the most stable.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)


(b) In a nuclear reactor, a nucleus of uranium(U)-235 fissions into barium(Ba)-141 and krypton(Kr)-92.

The equation for this fission is

nKrBaU 10

9236

14156

23592 x .

(i) Use the graph to show that the fission of one nucleus of uranium-235 will release about 200

MeV of energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(ii) State the value of x in the equation.

........................................................................................................................... (1)

(iii) The mass defect in this reaction is 3.1 × 10–28

kg. Calculate the number of uranium-235 nuclei

that must fission in order to release 1.0 kJ of energy.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)


(iv) Outline how this fission reaction can lead to a chain reaction.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) Intensive scientific effort is devoted to developing nuclear fusion as a future energy source. Discuss

what could be the social and environmental benefits of using nuclear fusion as compared with nuclear

fission as an energy source.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 15 marks)


244. This question is about quantum physics and electrons.

(a) Photons of frequency 2.1× 1015

Hz strike the surface of uranium and electrons are emitted from the

surface. The work function of uranium is 3.6 eV.

(i) Show that the maximum kinetic energy of the emitted electrons is about 5.0 eV.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(ii) Explain what change to this energy would occur if the light intensity was doubled.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(b) The de Broglie wavelength of an electron with energy 5.0 keV is λ.

(i) Determine λ.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)


(ii) A student makes the statement “The electron wavelength is not real, it is just a mathematical

construction. Electrons are particles and never waves.” Outline evidence which suggests that the

student’s statement is not correct.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) Outline how the

(i) “electron in a box” model accounts for the existence of discrete energy levels in the hydrogen

atom.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) line spectra of atomic hydrogen provide evidence for electron energy levels in the atom.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 14 marks)



A nucleus of the isotope iodine-124 (I-124) (proton number 53) may undergo positive beta decay to a nucleus

of an isotope X.

(a) State the nuclear reaction equation for this decay.

......................................................................................................................................

...................................................................................................................................... (3)

(b) The half-life of iodine-124 is 4.2 days. A freshly prepared sample of the isotope has an activity of 810

Bq. Determine the activity of the sample after 6.0 days.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 6 marks)

246. Radioactive decay

(a) Carbon-14 is a radioactive isotope with a half-life of 5500 years. It is produced in the atmosphere by

neutron bombardment of nitrogen. The equation for this reaction is

X.CnN 14

6

1

0

14

7

(i) Explain what is meant by isotopes.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Identify the particle X.

......................................................................................................................... (1)


(b) Each gram of a living tree contains approximately 4 1010

atoms of carbon-14.

On the axes below, draw a graph to show the variation with time of the number of carbon-14 atoms in

one gram of wood from a tree. Your graph should indicate the number of atoms for a period of 1.8

104 years after the tree has died. (Half-life of carbon-14 = 5500 years)

(3)

(c) The activity of a radioactive sample is proportional to the number of atoms in the sample. The activity

per gram of carbon from a living tree is 9.6 disintegrations per minute. The activity per gram of carbon

in burnt wood found at an ancient campsite is 1.9 disintegrations per minute.

(i) Estimate the number of atoms of carbon-14 in the burnt wood.

.........................................................................................................................

......................................................................................................................... (1)

(ii) From the graph you have drawn in (b), estimate the age of the burnt wood.

......................................................................................................................... (1)

(Total 7 marks)


247. This question is about wave-particle duality.

(a) Describe the de Broglie hypothesis.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) An electron is accelerated from rest through a potential difference of 1250 V. Determine the associated

de Broglie wavelength of the accelerated electron.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)

(Total 6 marks)

248. This question is about line spectra.

(a) Light is emitted from a gas discharge tube. Outline briefly how the visible line spectrum of this light

may be obtained.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)


(b) The table below gives information relating to three of the wavelengths in the line spectrum of atomic

hydrogen.

Wavelength / 10−9

m Photon energy / 10−19

J

1880 1.06

656 3.03

486 4.09

Deduce that the photon energy for the wavelength of 486 10−9

m is 4.09 10−19

J.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) The diagram below shows two of the energy levels of the hydrogen atom, using data from the table

above. An electron transition between these levels is also shown.

(i) On the diagram above, construct the other energy level needed to produce the energy changes

shown in the table above. (1)

(ii) Draw labelled arrows to represent the energy changes for the two other wavelengths shown in

the table above. (1)

(Total 6 marks)



In an experiment to investigate the photoelectric effect, light of frequency f is incident on the metal surface A

shown in the diagram below. A potential difference is applied between A and electrode B. The photoelectric

current is measured by the microammeter. (Note: the complete electrical circuit is not shown.)

(a) Indicate on the diagram the polarity of A and of B. (1)

(b) The frequency f of the light is reduced and it is found that there is a frequency f0, the threshold

frequency, below which the microammeter does not indicate a current. Explain how Einstein’s

photoelectric theory accounts for this observation.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)


(c) The potential difference between A and B is now reversed. For a particular frequency of the light, the

potential difference is changed until there is zero current in the circuit. The graph below shows the

variation of frequency f of the light with the potential difference, Vs, for zero current.

Explaining your working, use the graph to determine the

(i) threshold frequency.

.........................................................................................................................

......................................................................................................................... (1)

(ii) work function, in eV, of the metal.

.........................................................................................................................

......................................................................................................................... (2)

(Total 8 marks)

250. Which of the following gives the correct number of protons and neutrons in a nucleus of carbon-14 ( C146 )?

Protons Neutrons


A. 8 6

B. 6 8

C. 14 6

D. 6 14

(Total 1 mark)

251. Which of the following causes the greatest number of ionizations as it passes through 1 cm of air?

(The total energy of the ionizing radiation is the same.)

A. An alpha particle

B. A beta particle

C. A gamma-ray

D. An X-ray (Total 1 mark)


252. Emission and absorption spectra provide evidence for

A. the nuclear model of the atom.

B. natural radioactivity.

C. the existence of isotopes.

D. the existence of atomic energy levels. (Total 1 mark)

253. Which of the following is true in respect of both the Coulomb interaction and the strong interaction between

nucleons in an atom?

Coulomb interaction exists

between

Strong interaction exists

between

A. protons only neutrons only

B. both protons and neutrons neutrons only

C. protons only both protons and neutrons

D. both protons and neutrons both protons and neutrons

(Total 1 mark)

254. Which of the following correctly identifies the three particles emitted in the decay of the nucleus Ca4520 into

a nucleus of Sc4521 ?

A. α, β–, γ

B. β–, γ, v

C. α, γ, v

D. α, β–, v

(Total 1 mark)


255. The nuclear reaction

n He H H 10

42

31

21

is an example of

A. nuclear fission.

B. radioactive decay.

C. nuclear fusion.

D. artificial transmutation. (Total 1 mark)

256. An alpha particle is accelerated through a potential difference of 10 kV. Its gain in kinetic energy is

A. 10 eV.

B. 20 eV.

C. 10 keV.

D. 20 keV. (Total 1 mark)

257. Which of the following decay sequences would result in the daughter nucleus having the same proton number

as the parent nucleus?

A. Alpha followed by gamma

B. Beta (β–

) followed by gamma

C. Alpha followed by beta (β–) followed by beta (β

–)

D. Beta (β–) followed by gamma followed by gamma

(Total 1 mark)


258. The difference between the mass of a C126 nucleus and the sum of the masses of the individual nucleons is

0.1 u. Which of the following is approximately the binding energy of the nucleus?

A. 90 MeV

B. 90 MeV c–2

C. 8 MeV

D. 8 MeV c–2

(Total 1 mark)

259. The process by which a heavy nucleus splits into two lighter nuclei is known as

A. fission.

B. fusion.

C. radioactive decay.

D. artificial (induced) transmutation. (Total 1 mark)

260. The Geiger–Marsden experiment provides evidence for

A. the existence of discrete atomic energy levels.

B. the existence of the neutron.

C. a dense positively charged nucleus.

D. the stability of some nuclei. (Total 1 mark)


261. A radioactive isotope has a half-life of two minutes. A sample contains sixteen grams of the isotope. How

much time elapses until one gram of the isotope remains?

A. 6 minutes

B. 8 minutes

C. 10 minutes

D. 12 minutes (Total 1 mark)

262. Data concerning nuclides are plotted using the axes below.

What are the axis labels for this graph?

Y X

A. binding energy per nucleon number of nucleons

B. binding energy number of protons

C. number of protons binding energy per nucleon

D. number of nucleons binding energy

(Total 1 mark)


263. Which of the following is true about beta minus (β–) decay?

A. An antineutrino is absorbed.

B. The charge of the daughter nuclide is less than that of the parent nuclide.

C. An antineutrino is emitted.

D. The mass number of the daughter nuclide is less than that of the parent nuclide. (Total 1 mark)

264. The number of neutrons and the number of protons in a nucleus of an atom of the isotope of uranium U23592

are

Neutrons Protons

A. 92 143

B. 143 92

C. 235 92

D. 92 235

(Total 1 mark)

265. A sample contains an amount of radioactive material with a half-life of 3.5 days. After 2 weeks the fraction

of the radioactive material remaining is

A. 94 %.

B. 25 %.

C. 6 %.



266. The rest mass of a proton is 938 MeV c–2

. The energy of a proton at rest is

A. 9.38 J.

B. 9.38 × 108 × (3 ×10

8)2 J.

C. 9.38 × 108 eV.

D. 9.38 × 108 × (3 × 10

8)2 eV.

(Total 1 mark)

267. The Geiger-Marsden experiment (scattering of alpha particles) provided evidence for

A. the nature of alpha particles.

B. orbital electrons in the atom.

C. very small and relatively massive nucleus.

D. the existence of atomic energy levels. (Total 1 mark)

268. A nuclear reaction is represented by the following equation.

HAuHgn 21

19779

19880

10

This reaction is an example of

A. fission.

B. fusion.

C. natural transmutation.

D. artificial (induced) transmutation. (Total 1 mark)


269. Which of the following graphs best shows the variation with nucleon number N of the binding energy per

nucleon E?

(Total 1 mark)

270. The relationship between proton number Z, neutron number N and nucleon number A is

A. A = Z – N.

B. Z = A + N.

C. N = A – Z.

D. N = A +Z. (Total 1 mark)


271. In the Geiger–Marsden experiment α-particles are scattered by gold nuclei. The experimental results provide

evidence that

A. α-particles have discrete amounts of kinetic energy.

B. most of the mass and positive charge of an atom is concentrated in a small volume.

C. the nucleus contains protons and neutrons.

D. gold atoms have a high binding energy per nucleon. (Total 1 mark)

272. A radio-isotope has an activity of 400 Bq and a half-life of 8 days. After 32 days the activity of the sample is

A. 200 Bq.

B. 100 Bq.

C. 50 Bq.

D. 25 Bq. (Total 1 mark)

273. The binding energy per nucleon of the nucleus Li7

3 is approximately 5 MeV. The total energy required to

completely separate the nucleons of this nucleus is approximately

A. 15 MeV.

B. 20 MeV.

C. 35 MeV.

D. 50 MeV. (Total 1 mark)


274. The initial activity of a sample of a radioactive isotope of half-life 10 hours is A. What is the age of the

sample when its activity is ?32

A

A. 30 hours

B. 40 hours

C. 50 hours

D. 320 hours (Total 1 mark)

275. When the isotope aluminium-27 is bombarded with alpha particles, the following nuclear reaction can take

place.

neutronXAlHe 27

13

4

2

Which of the following correctly gives the atomic (proton) number and mass (nucleon) number of the

nucleus X?

Proton number Nucleon number

A. 15 30

B. 16 31

C. 30 15

D. 31 16

(Total 1 mark)


276. A brick is placed on the surface of a flat horizontal disc as shown in the diagram below. The disc is rotating

at constant speed about a vertical axis through its centre. The brick does not move relative to the disc.

Which of the diagrams below correctly represents the horizontal force or forces acting on the brick?

(Total 1 mark)


277. A frictionless trolley of mass m moves down a slope with a constant acceleration a. A second similar

frictionless trolley has mass 2m. The acceleration of the second trolley as it moves down the slope is

A. .2

1a

B. a.

C. 2a.

D. 4a. (Total 1 mark)


The frequency f of the fundamental vibration of a standing wave of fixed length is measured for different

values of the tension T in the string, using the apparatus shown.


In order to find the relationship between the speed v of the wave and the tension T in the string, the speed v is

calculated from the relation

v = 2 f L

where L is the length of the string.

The data points are shown plotted on the axes below. The uncertainty in v is ±5 m s–1

and the uncertainty in T

is negligible.

(a) Draw error bars on the first and last data points to show the uncertainty in speed v. (1)

(b) The original hypothesis is that the speed is directly proportional to the tension T.

Explain why the data do not support this hypothesis.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)


(c) It is suggested that the relationship between speed and tension is of the form

v = k T

where k is a constant.

To test whether the data support this relationship, a graph of v2 against T is plotted as shown below.

The best-fit line shown takes into account the uncertainties for each data point.

The uncertainty in v2 for T = 3.5 N is shown as an error bar on the graph.

(i) State the value of the uncertainty in v2 for T = 3.5 N.

...........................................................................................................................

........................................................................................................................... (1)

(ii) At T = 1.0 N the speed v = 27 ± 5 m s–1

. Calculate the uncertainty in v2.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)


(d) Use the graph in (c) to determine k without its uncertainty.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

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......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(Total 11 marks)

Documents

IB Physics Semester 1 Exam Review