1

Name : _______________________________ CT group: ____________

VICTORIA JUNIOR COLLEGE 2011 JC2 PRELIMINARY EXAMINATIONS

PHYSICS Higher 2 Paper 2 Structured Questions

Candidates answer on the Question Paper No Additional Materials are required.

9646/02

20 Sep 2011TUESDAY

2 pm – 3.45 pm1 Hour 45 minutes

For Examiner’s Use

1

2

3

4

5

6

7

Total (max. 72)

READ THESE INSTRUCTIONS FIRST Write your name and CT group at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

This document consists of 22 printed pages.

2

Data speed of light in free space, c = 3.00 × 108 m s-1 permeability of free space, µo = 4π × 10-7 H m-1 permittivity of free space, εo = 8.85 × 10-12 F m-1 (1/(36π)) × 10-9 F m-1 elementary charge, e = 1.60 × 10-19 C the Planck constant, h = 6.63 × 10-34 J s unified atomic mass constant, u = 1.66 × 10-27 kg rest mass of electron, me = 9.11 × 10-31 kg rest mass of proton, mp = 1.67 × 10-27 kg molar gas constant, R = 8.31 J mol-1 K-1 the Avogadro constant, NA = 6.02 × 1023 mol-1 the Boltzmann constant, k = 1.38 × 10-23 J K-1 gravitational constant, G = 6.67 × 10-11 N m2 kg-2 acceleration of free fall, g = 9.81 m s-2

3

Formulae uniformly accelerated motion, s = ut + (½) at2 v2 = u2 + 2as work done on/by a gas, W = pΔV hydrostatic pressure, p = hρg gravitational potential,

rGM

−=φ

displacement of particle in s.h.m., x = xo sin ω t velocity of particle in s.h.m.,

)(

cos22 xx

tvv

o

o

−±=

=

ω

ω

resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2+ … electric potential, V = Q/4πεor alternating current/voltage, x = xo sin ω t transmission coefficient, T ∝ exp(-2kd)

where 2

2 )(8h

EUmk −=

π

radioactive decay, x = xo exp(-λt) decay constant,

21

693.0t

=λ

4

1. A stuntsman decides to ride his motorcycle from a ramp of height 1.0 m inclined at an angle of 30.0o to the horizontal to the top of a stationary carriage of height 4.0 m and at a distance of 10.0 m from the edge of the ramp.

Fig. 1.1 (a) Assuming that the motorcycle is a point mass, calculate its minimum speed of

take-off from the ramp in order for it to just land on the top of the carriage. [4]

Take-off speed = …………… m s-1

(b) Calculate the velocity of the motorcyclist 0.50 s after takeoff from the ramp.. [4]

velocity = …………… m s-1 at angle _____ to horizontal

30.0o

1.0 m

10.0 m

4.0 m carriage

5

2. The variation with current of the potential difference V across a component X is shown in Fig. 2.1.

(a) Explain how the resistance of component X is obtained from the graph for a

given potential difference. [1] ………………………………………………………………………………… ………………………………………………………………………………… …………………………………………………………………………………

(b) Calculate the largest resistance of component X in the range of currents shown in Fig. 2.1. [2]

Resistance = …………. Ω (c) The component X and the resistor R of resistance 5.0 Ω are connected in series

with a battery of internal resistance r as shown in Fig. 2.2.

5.0 Ω X

R

Fig. 2.2

The current in the circuit is found to be 2.0 A.

Fig. 2.1

V / V

6

(i) Use Fig. 2.1 to determine the potential difference across component X. [1]

p.d. = ...................... V

(ii) Determine the internal resistance r of the battery given that its e.m.f. is 16.0 V. [2]

r = ..................... Ω

(d) The resistor R and the component X are now connected in parallel with the battery, as shown in Fig. 2.3. Comment qualitatively on how this will affect the magnitude of the current from the battery as compared to the arrangement in (c). [2]

………………………………………………………………………………… ………………………………………………………………………………… …………………………………………………………………………………

………………………………………………………………………………… ………………………………………………………………………………… …………………………………………………………………………………

X R 5.0 Ω

Fig. 2.3

7

3. (a) State what is observed when a beam of white light passes through a diffraction grating. [1]

………………………………………………………………………………… ………………………………………………………………………………… …………………………………………………………………………………

(b) A beam of white light is allowed to fall normally onto a diffraction grating with 300 lines per millimeter. Assume that the light source consists of wavelengths between 400 nm and 700 nm.

(i) Determine the highest order of the full spectrum that can be produced in this case. [3]

maximum order = ………………..

(ii) Calculate the largest diffraction angle for the 700 nm wavelength using this grating. [1]

Diffraction angle = ……………….

8

(iii) Show mathematically that the first- and second-order spectra do not overlap. On Fig. 3.1, draw the 400 nm and 700 nm light beams of the first- and second-order spectra between the grating and the screen to illustrate what is observed. [3]

Fig. 3.1

grating

screen

white light beam

9

4. A straight metal rod PQ of mass m equal to 15.0 g and length l equal to 12.2 cm is suspended from a spring of constant k, in a magnetic field of flux density 1.02 T. The spring stretches a distance of 5.0 cm under the weight of the rod. It is then stretched a further distance of 3.0 cm before being released. When oscillating, its

period T is given by kmT π2= . (Assume negligible air resistance.)

(a) Calculate the period of oscillation of the rod. [2]

Period = ………………. s

(b) Calculate the maximum e.m.f. induced in the rod. [3]

Maximum induced e.m.f. = ………………. V

(c) Sketch a graph of the induced e.m.f. against time from the instant of release of the rod. Label all numerical values on your graph. [2]

(d) State which end of the rod, P or Q, is at a higher potential when it is moving upwards. [1]

…………………………………………………………………………………

P Q

5.0 cm

3.0 cm

Fig. 4.1

B (out of page)

10

5. (a)(i) State one observation from Einstein’s photoelectric experiment that led to the conclusion that light has particle-like properties. [1]

……………………………………………………………………………….

(ii) Explain the reasoning behind your conclusion in (a)(i). [1]

………………………………………………………………………………….. ………………………………………………………………………………….. …………………………………………………………………………………..

(iii) Write down Einstein’s photoelectric equation, identifying each of the three terms in it. [2]

………………………………………………………………………………….. ………………………………………………………………………………….. …………………………………………………………………………………..

(b) In a photoelectric experiment, light of various frequencies was shone onto a metal surface, and the stopping potential Vs was measured in each case. The resulting graph of stopping potential against frequency is shown in Fig. 5.1.

Fig. 5.1

f / 1014 Hz

Vs / V

0.30

0.50

0.70

0.90

4.0 5.0 6.0 7.0

11

(i) Determine the threshold frequency for the metal. (Note that the graph in Fig. 5.1 does not start from the true origin.) [3]

Threshold frequency = ………………. Hz

(ii) Determine the work function of the metal. [1]

Work function = ………………. J

12

6. An alpha particle (α-particle) is the nucleus of the helium ( He42 ) atom. It is

produced by the decay of a radioactive atom or nuclide. As the α-particle passes through matter, it loses kinetic energy. The distance travelled by the α-particle up to the point where its energy is almost totally depleted is called the range of the particle. The energy of the alpha particle is measured in mega-electron-volts (MeV).

(a) Suggest how the α-particle loses energy as it passes through matter. [2]

………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. …………………………………………………………………………………..

(b) Discuss whether the range of α-particles in liquids would be different from that

in air. [2] ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. …………………………………………………………………………………..

(c) Calculate the momentum of an α-particle of kinetic energy 5.68 MeV. [2]

Momentum = ………………. kg m s-1.

13

In the early part of the twentieth century, experiments were carried out to measure the range and kinetic energies of α-particles in air using a number of different radioactive nuclides. Data relating to the range R and the kinetic energy E of α-particles emitted from 5 different nuclides P, Q, R, S and T are given in Fig. 6.1.

Fig. 6.1

It is suggested that R and E are related by the equation

R = cEn

where c and n are constants.

(d) (i) Given the data in Fig. 6.1, suggest a suitable graph that should be plotted to test the validity of the equation between R and E. [1]

………………………………………………………………………………

(ii) Without changing the units of R and E given in Fig. 6.1, calculate suitable values of quantities involving R and E and complete the last two columns in the table that will permit you to plot a straight-line graph. [2]

(iii) In Fig. 6.2 on page 14, plot a suitable graph and use it to determine the

values for c (to 3 significant figures) and n (to 2 significant figures). Include appropriate units in your answers where applicable. [5]

Working to find c and n:

c = ……………..

n = ……………..

nuclide R / cm E / MeV

P 4.00 5.38

Q 4.35 5.68

R 4.80 6.05

S 5.05 6.28

T 5.70 6.77

14

Fig. 6.2

15

(e) (i) A nuclide Z emits an α-particle of energy of 6.00 MeV. Using your graph in Fig. 6.2, or otherwise, estimate the range of this alpha particle in air. [2]

Range = …………….. cm

A scientist suggests that the range Ra of an α-particle in air of density ρa is related to the range Rm of the same particle in another medium of density ρm and relative atomic mass Am by the following formula:

m

mmaa A

RR

ρρ 82.3=

The following data are known: Density of air: 1.3 kg m-3 Density of aluminium: 2700 kg m-3 Relative atomic mass of aluminium = 27

(ii) Calculate the thickness of aluminium foil required to stop the α-particles emitted from nuclide Z. [2]

Thickness = …………….. m (iii) α-particles are not able to penetrate the human skin. Discuss whether

α-particles do not therefore pose a threat to human health. [2]

……………………………………………………………………………... ……………………………………………………………………………... ……………………………………………………………………………... ……………………………………………………………………………... ……………………………………………………………………………...

16

7. Modern day lifts in tall buildings are of a relatively simple design. A passenger car is connected to a counterweight by a steel cable which passes over a system of pulleys at the top of the lift shaft, as shown in Fig. 7.1.

The passenger car and the counterweight are of similar mass. A motor, which is connected to the pulley system, is used to raise and lower the passenger car. A braking system enables the passenger car to come to rest at any desired position. If both the motor and the braking system were to fail, the passenger car and counterweight would move under the action of gravity until one of several safety features incorporated into the design of the system (not shown on Fig. 7.1) brings the passenger car and counterweight to rest.

A failure of the motor and braking system may be simulated in the laboratory by connecting two objects A and B of mass mA and mB respectively by a thin steel wire which passes over a pulley, as shown in Fig. 7.2.

Fig. 7.1

Fig. 7.2

17

Design a laboratory experiment to investigate how the acceleration of object A depends on the mass mB of object B when the system is allowed to move freely under the action of gravity. You may assume that mA is constant throughout and that mA > mB. You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to

(a) the equipment you would use,

(b) the procedure to be followed,

(c) the measurements that would be taken,

(d) the control of variables,

(e) two precautions that would be taken to improve the accuracy of the experiment.

(f) two safety precautions in this experiment.

[12] Diagram

18

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..

19

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..

20

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..

21

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..

22

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..