FIGURE 1 - YSL Physics - Homeyslphysics.weebly.com/uploads/4/8/2/6/48261583/sep_sem_1.pdf · ... A boy rides a bicycle along a straight line from his house to a ... by the car when

Synergizing Excellence Project

Physic’s Unit, KML 1

2.0: KINEMATIC OF LINEAR MOTION

QUESTION 1

(a) A boy rides a bicycle along a straight line from his house to a store 1000 m away. On

his way back, he stops at a friend’s house which is halfway between his house and the

store. Determine the displacement and the distance he has traveled?

(500 m, 1500 m)[3marks]

(b)

A car moves along a straight line so that its distance from some starting point varies

with time as described by the graph of FIGURE 1.

(i) Sketch velocity against time graph.

(ii) Is the instantaneous velocity at point A greater or less than that at point B?

Explain. [4 marks]

(c)

Describe the motion of the graph shown in FIGURE 2 by using the elements of

velocity and acceleration. [3 marks]

(d)

FIGURE 1

FIGURE 2

FIGURE 3



A researcher finds in the performance data for his new car the velocity-versus-time

graph shown in the FIGURE 3.

(i) Calculate the average accelerations of the car during the segments II and

III respectively. (0 ms-2

, -2.5 ms-2

)

(ii) Determine the distance traveled by the car when it is moving at constant speed.

(180 m)[5 marks]

QUESTION 2

(a) A marble rolls across a flat surface in direction of positive x-axis. Its

initial speed is 1 m s-1

but it comes to rest after 10 seconds.

Calculate:

(i) the acceleration of the marble. (-0.1 ms-2

)

(ii) the distance travelled by the marble as it comes to rest. (5 m)[4 marks]

(b) Sketch a displacement – time graph to show the motion of a ball thrown vertically

upwards from the ground until it reaches at maximum height, H and later fall to the

ground by assuming the ball is under free fall motion. [2 marks]

(c) A ball is thrown upward from the ground with an initial speed of 25 m s-1

; at the same

instant, another ball is dropped from a building 15 m high. After how long will the

balls be at the same height? Neglect air resistance. (0.6 s)[4 marks]

QUESTION 3

A youngster hurls a ball horizontally at speed of 10 m s-1

from a bridge 50 m above a river.

Ignore air resistance.

(a) How long will it take for the ball to hit the water? (3.19 s)[3 marks]

(b) What is the velocity of the ball just before it lands? (33 ms-1

, 72o) [6 marks]

(c) How far from the bridge will it strike? (3.19 m)[1 mark]



3.0: MOMENTUM & IMPULSE

QUESTION 1

a) i. What is meant by linear momentum?

ii. A 1.5 kg ball moving with an initial speed of 35 m s-1

hits a door and rebound

with the same speed. Calculate the impulse on the ball. (10.5 kg m s-1

)

b) You drop a 12 g ball as in FIGURE 1 above from a height of h = 1.2 m and it only

bounces back to a height of h’ = 0.7 m

i. What is the initial momentum and the final momentum of the ball?

(- 0.0582 kg m s-1

, 0.0444 kg m s-1

)

ii. What is the total impulse on the ball when it hit the floor and states the type of the

collision? (0.1027 kg m s-1

)

h h'

vA vA’

FIGURE 1



QUESTION 2

a) i. States the principle of conservation of momentum

ii. State the condition for elastic and in-elastic collision

b) i. Figure 2 shows two discs with the same mass travelling perpendicular to each

other, Disc A travelling with a constant velocity of 50 m s-1

to the right. Let say,

disc B has a velocity of 40m s-1

just before it hits the disc A and stuck to disc A.

Determine the combine velocity of the disc and the direction of the motion after

the collision. (35.02 ms-1

,38.66o )

ii. A boy is standing on the middle of his skate board. Initially both the boy and the

skate are at stationary and then the boy start to walk to the front edge of the

board, what would happen to the skateboard? Does it stay stationary, move with

the boy or move backward, justify your answer.

VB=40 m s-1

VA=50 m s-1

Disc A

Disc B

Disc B

Disc A

FIGURE 2



4.0: FORCES

QUESTION 1

b) state 5 types of forces

c) i) An object with mass m1 rests on a frictionless horizontal table and is connected to

a cable that passes over a pulley and is then fastened to a hanging object with

mass m2. Draw free body diagram for the each mass below.

ii) Draw free body diagram for the hanging thief below

d) Two people are pulling a boat through the water as in FIGURE 1. Each exerts a force

of 600 N directed at a 30o angle relative to the forward motion of the boat. If the boat

moves with constant velocity, find the resistive force exerted by the water on the boat.

(1039.2 N)

FIGURE 1

FIGURE 1



QUESTION 2

The forces F1 = F2 = F3 = 8 N and F4 act on a particle O as shown in FIGURE 2. The particle

remains in static equilibrium

Find

a) The magnitude of the force F4

b) the value of α

QUESTION 3

a) A box which has a mass of 10 kg is pulled by a person with a force of 40N, and it is

exerted at a 300 angle as shown in FIGURE 3. Kinetic coefficient of friction given as

0.2.

Based on the information given, draw a free body diagram and determine

i. Normal force acting on the block. (78.1N)

ii. Kinetic frictional force. (15.62N)

iii. The acceleration of the box. (1.9ms-2

)

FIGURE 3

FIGURE 2



b) A box of mass 25kg is placed on an inclined surface that makes an angle 300 as shown

in FIGURE 4.

Based on the information given, draw a free body diagram if the block slides down

with constant velocity and determine

i. Normal force acting on the block (212.39N)

ii. Frictional force acting on the block (122.63N)

iii. Kinetic coefficient of friction (0.58)

iv. If the block is pulled up the inclined plane with a 2kN force which is parallel

with the plane, determine the acceleration of the block. (70.19ms-2

)

30O

FIGURE 4



5.0: WORK, ENERGY & POWER

QUESTION 1

e) i) Define work done.

ii)

FIGURE 1 shows a spring with spring constant, being

compressed by a constant force, . Find amount of work done by the spring’s

restoring force if the spring is compressed by . (1600 J)

f) i) State ONE difference and ONE similarity between potential and kinetic energy.

ii) A ball is thrown vertically upward by a baseball player and reaches the highest

point of above him. By using the principle of conservation of energy,

calculate the speed of the ball when it leaves the player’s hand. (44.29 ms-1

)

QUESTION 2

a) FIGURE 2 shows a wind turbine used to produce electricity. The turbine blades are

turned by the wind and are connected to an electrical generator.

i) State the useful energy transformations that occur during the operation of a wind

turbine.

ii) In one revolution the blades sweep out a circle, in 60s a volume of 540 000 m3 of

air travelling at a speed of 60 m s-1

is incident at right angles on that circle.The

density of air is 1.2 kg m-3

. Calculate the maximum input power available to the

wind turbine. (1.9 x 107 W)

FIGURE 1

FIGURE 2



b) A 70 kg base-runner(base-ball competition) begins to slide into second base when

moving at a speed of 4.0 m/s. The coefficient of kinetic friction between his clothes

and the earth is 0.70. He slides so that his speed is zero just as he reaches the base

i) How much energy is lost due to friction acting on the runner? (-560 J)

ii) How far does he slide? (1.17 m)

QUESTION 3

a) i) Show that power may be expressed as product of force and velocity (P = F.v)

ii) A car engine has a maximum power of 110kW, find the possible tractive (pulling)

force at 10 m s-1

and at 30 m s-1

. (11.0 kN, 3.7 kN)

b) Each time the heart pumps it accelerates about 20g of blood from 0.20 m s-1

to 0.34

ms-1

.

i) What is the increase in kinetic energy of the blood with each beat? (7.6 x 10-4

J)

ii) Calculate the power of the heart when it beats at about 80 beats per minute.

(1.0 mW)



6.0: CIRCULAR MOTION

1 (a) Define uniform circular motion.

(b) The Earth rotates about a vertical axis every 8.6x104 s. If an object is at the

equator, calculate

(i) its angular velocity, (7.3 x 10-5

rad s-1

)

(ii) its linear speed, (467.2 m s-1

)

(iii) its acceleration due to the rotation of the earth’s axis. (0.034 rad s-2

)

(c) An object of mass 4kg is whirled around in a vertical circle of radius 2.0 m at a

speed of 5 ms-1

.

(i) Draw a free body diagram at the top and bottom of the circle.

(ii) Calculate the maximum and minimum tension in the string connecting

the object to the centre of the circle. (89.24 N, 10.76 N)

2 (a) (i) Define centripetal acceleration.

(ii) Calculate the centripetal acceleration of an object at equator due to

rotation of earth. The radius of earth is 6.4x106 m. (3.38 X 10

-2 ms

-2)

(b) (i) Explain why the car needs a horizontal force to turn the corner and

where this force comes from?

(ii) A van of mass M kg negotiates a circular road whose radius is 100 m.

If the frictional force between its tyres and the road is 0.5 times its

weight. What is the maximum speed at which the van can safely

negotiate the curve without skidding? (22.15 ms-1

)



7.0: GRAVITATION

1 (a) State Newton’s Law of Gravitation.

(b) A space probe of mass 1800 kg is travelling from the Earth to the Mars. The

space probe is midway between the planets. Use the data given to find

(i) the gravitational force on the space probe due to the planet Earth

(ii) the gravitational force on the space probe due the planet Mars

(iii) the acceleration of the space probe due to the gravitational forces

acting on it

(Separation between the Earth and the Mars = 7.80 X 1010

m, Mass of the

Earth = 6.00 X 1024

kg, Mass of the Mars = 6.40 X 1023

kg)

(4.74 x 10-4

N, 5.05 x 10-5

N, 2.35 x 10-7

ms-2

)

(c) The gravitational force acting on a 400 kg motorcycle on the surface of planet

A is 3200 N. The radius of planet B is twice that of planet A. The two planets

have the same mass. What is the gravitational force acting on the same 400 kg

motorcycle placed on the surface of planet B? (800 N)

2 (a) Define gravitational potential, V

(b) (i) Show that

(ii) Find the the ratio of gravitational potential on the Moon’s surface to

that on Earth’s surface. Given the mass of the Earth is 246.0 10 kg and

its radius is66.4 10 m . The moon has a mass of

227.4 10 kg and its

radius is 1700 km. (0.0464)

(b) Sketch a graph to show the variation of the gravitational potential, V with

distance r from the centre of the earth. Mark the radius of the earth as R in

your graph.



3 (a) Show that tangential speed, √

and √

for a

motion of satellite in circular orbit.

(b) The distance between the International Space Station and the Earth surface is

356 km. Given the mass of the Earth is 246.0 10 kg and its radius is

66.4 10 m . Calculate the,

(i) Speed of the space station. (7.7 x 103 ms

-1)

(ii) Period of the space station orbiting the Earth. (5515 s)

(iii) Gravitational potential at the space station. (5.92 x 107 J kg

-1)

(c) Two satellites are in circular orbits around the Earth. Satellite A is at an

altitude equal to the Earth’s radius, while satellite B is at an altitude equal to

twice the Earth’s radius. What is the ratio of their periods, TB/TA? (1.84)



21

2CMI MR

21

2I MR

8.0: ROTATIONAL OF RIGID BODY

1 (a) Define torque.

(b)

A frictional force of 70 N between a wheel and a horizontal surface slows

down the rotation of the wheel. The radius of the wheel is 40 cm and its mass

is 50 kg.

(Assume the moment inertia wheel, )

(i) What is the torque on the wheel? (28 Nm)

(ii) The initial angular velocity of the wheel is 2.4 revolutions per second.

What is the time taken for the wheel to stop? (2.15 s)

(iii) How many revolutions does the wheel makes before it stop? (2.59 rev)

(iv) Calculate the work done against friction? (454.72 J)

2 (a) (i) Define moment of inertia of a rigid body.

(ii) A torque of 15 N m constantly acts on a wheel that spins 150

revolutions in 20 s. Calculate the average power delivered to the

wheel. (706.9 W)

(b) (i) State the principle of conservation of angular momentum.

(ii) A turntable of mass 2.4 kg and diameter 40 cm is spinning with an

angular velocity of 45 revolutions per minute. A small piece of

plasticine of mass 200 g is dropped and stuck to the turntable at a

distance of 10 cm from the axis of rotation. Calculate the new angular

velocity. (4.52 rad s-1

)

(The moment of inertia of the turntable is )

70 N R



3 A roll of toilet paper is held by the first piece and allowed to unfurl as shown in the

FIGURE 1. The roll has an outer radius R = 6.0 cm, an inner radius r = 1.8 cm, a

mass m = 200 g, and falls a distance s = 3.0 m. Assuming the outer diameter of the roll

does not change significantly during the fall, determine

(Moment of inertia for toilet paper roll, I =

m(R2 + r2) )

r

R

FIGURE 1

(a) the tension in the sheets (0.693 N)

(b) the translational acceleration of the roll (6.34 ms-2

)

(c) the angular acceleration of the roll (16.8 rev s-2

)

(d) the final translational speed of roll (6.17 ms-1

)

s



9.0: SIMPLE HARMONIC MOTION

1 (a) Define simple harmonic motion.

(b) The diagram shows one piston of an internal combustion engine

As the crankshafts rotates through 360°, the top of the piston moves from L to

T and back to L. The distance of LT is 9.6 cm and the crankshaft rotates at

3600 revolutions per minute. Calculate

i) the frequency of oscillations, f of the piston (60 Hz)

ii) amplitude of this oscillation. (0.048 m)

iii) The maximum acceleration of the piston if the oscillations of the piston

are approximately simple harmonic (6821.87 ms-2

)

iv) At which position(s) in movement of the piston will this acceleration

be zero?

2 (a) Sketch the x against t graph for the following expression:

(b) A particle undergoes SHM on a straight line with amplitude 3.0 cm and

frequency 5.0 Hz. Write down an expression for the displacement of the

motion if the particle is +1.0 cm from the equilibrium at t = 0 s. Assume that

displacement to the right side of the equilibrium position is positive.

(c) The length of the string of a simple pendulum is 1.5 m. Determine the

percentage change in the period of oscillation if the pendulum initially at a

place where the gravitational field strength is 9.80 N kg-1

is brought to another

place where the gravitational field strength is 9.78 N kg-1

. (0.10 %)

crankshafts

T

L

2 2sincm 5

πtx



10.0: MECHANICAL WAVES

1 a) i) Define wave number.

ii) Distinguish between particle vibrational velocity and wave propagation

velocity.

b) A transverse wave on a string is given by y (x,t) = 2.4 sin [

( )]

where both x and y are in centimeters.

i) Sketch a graph of displacement against time for 0 ≤ t ≤ 2T

ii) Calculate the maximum velocity of the particle vibrating in the wave.

iii) What is the particle velocity at x = 1.5 cm and t = 0.25 s.

2 a) i) State the principle of superposition.

ii) Use the diagram to show how the constructive interference formed.

b) i) What is the other name of stationary waves?

ii) How stationary wave is formed?

c) State two differences between progressive waves and stationary waves.

d) The expression of a stationary wave is given by

1 4 150cos sin

2 5 2y x t

where y and x in metres and t in seconds.

i) Write the expression for the progressive waves that travels to the right

which resulting the stationary wave above.

ii) Determine the wavelength, frequency, amplitude and velocity for both

progressive waves.



11.0: SOUND WAVES

1 a) Define Sound intensity and state it’s SI Unit.

b) A point source produces sound with a power of 2kW .

i) What is the intensity of sound at a distance of 50cm and 100cm from the

source? (636.6 Wm-2

, 1570.8 Wm-2

)

ii) Find the ratio of the amplitude of the sound wave at 50cm to its amplitude at

100cm. (0.64)

2 a) A stationary wave is set up on a wire of length 0.93 m so that it vibrates at 120

Hz. The fundamental frequency of the wire is 40Hz.

i) Draw a sketch of the stationary wave obtained.

ii) Calculate the speed of the wave. (74ms-1

)

b) Stationary waves are set up in a tube closed at one end, and another tube open at

both ends. Both tubes are length of 34.0 cm.

i) Draw diagrams showing the stationary waves set up in both tubes for the

fundamental mode and second overtone

ii) Calculate the frequencies of the fundamental mode and the second overtone

for the open end tube (485.29 Hz, 1455.88 Hz)

[Speed of Sound = 330 m s-1

]

3 a) Define Doppler Effect.

b) An equation for the apparent frequency brought about by Doppler Effect for sound

is given by

Explain the symbol in the equation

c) An ambulance with its siren travels at 35 m s-1

. The frequency of the siren is 1700

Hz. What is the apparent frequency of the siren hear by a stationary observer

i) when the ambulance approaches him (1901.69 Hz)

ii) when the ambulance moves away from him (1536.98 Hz)

[Speed of Sound = 330 m s-1

]

S

S

OO f

vv

vvf



12.0: DEFORMATION OF SOLID

1 a) Distinguish between elastic deformation and plastic deformation.

b) On the same axes, sketch the stress-strain graph of a glass and a copper wire. Label

your graph clearly.

c) Define stress and strain for a stretched wire.

d) The figure below shows a 6.0 kg weight suspended by a 0.7 m vertical copper wire

with cross sectional area 4.5 mm2. A 4.0 kg weight is suspended by a similar wire

from the bottom of the 6.0 kg weight.

(Young’s modulus of copper is 1.0 × 1011

N m-2

)

i) Calculate the stress in each wire. (2.18 x 107 Pa, 8.72 x 10

6 Pa)

ii) Calculate the strain of each wire. (2.018 x 10-4

, 8.72 x 10-5

)

iii) Calculate the extension of each wire. (1.53 x 10-4

m, 6.10 x 10-5

m)

iv) Which wire will most likely be broken first? Give your reason.

2 a) With the aid of diagram, show that the strain energy stored in a stretched

material can be written as

where U is strain energy.

b) A copper rod has a diameter of 5 mm and is 30 cm long. It is subjected to a tensile

force of 100N as shown in the following figure. Find the strain energy stored in the

rod. The Young’s modulus for copper is 1.0 x 1011

Nm-2

.

(7.64 x 10-4

J)

c) A steel rod of radius 1 mm and length 81 cm is subjected to a force 100 kN. If the

Young’s modulus of steel is 2.0x1011

Pa, what is the elongation of the rod?

(0.129 m)

d) A piece of wire having cross sectional area A elongates by e when a weight W is

hung vertically from one end. If the area is increased to 2A when the weight is

increased to 2W, what would be the new elongation of the wire in terms of e?



13.0: HEAT

1 a) Define

i) heat conduction

ii) thermal conductivity

b) A uniform aluminium rod which is perfectly insulated has a cross-sectional

area of 2.50 cm2 and length 20.0 cm. Heat is conducted by the aluminium rod.

When the steady state is attained, the temperatures at the ends of the rod are

1200C 30

0C. Calculate

i) the temperature gradient along the rod (-450 oC)

ii) the rate of heat flow in the rod (23.6 W)

iii) the temperature 15.0 cm from the hot end. (52.5 oC)

( Thermal conductivity of aluminium = 210 W m-1

K-1

)

2 a) State ONE difference between temperature and heat.

b) A wall of dimension 4 m × 7 m consists of two layers made of two materials,

X and Y as shown in figure below. The temperature of the external surface of

the material X and Y is 55 ˚C and 40 ˚C respectively.

Thermal conductivity of material Y is six times of X .

Determine the temperature at the boundary of the two layers at constant heat

flow if the thickness of material X is 3.5 cm and the thickness of material Y is

8.5 cm. (44.3 oC)

c) Define the thermal equilibrium of two objects.

d) When a metal rod A of length 100 cm is heated from 0 ˚C to 100 ˚C, it

expands by 0.08 cm. Another metal rod B of the same length heated through

the same range of temperature expands by 0.035 cm.

i) Calculate the coefficient of linear expansion for metal A and B.

(3.5x10-6 o

C.1, 8 x 10

-6 oC

-1)

ii) A metal rod C which is a combination of metal A and B as shown in

figure below is heated from 0 ˚C to 100 ˚C. If it expands by 0.070 cm,

determine the initial length of the metals A and B. (0.778 m, 0.222 m)

X Y 55˚C 40˚C

3.5 cm 8.5 cm



14.0: KINETIC THEORY OF GASES

1 a) Sketch a pressure, P against volume, V graph of an ideal gas.

b) Gas is contained in an 8.00 L vessel at a temperature of 20.0°C and a pressure

of 9.00 atm. Determine the number of moles of gas in the vessel?

c) State the principle of equipartition of energy.

d) The molar mass of oxygen is 32 g mol-1

. At 500 K, find

i) the root mean square speed of the oxygen molecules,

ii) the internal energy of 5 moles of oxygen.

e) Explain why the internal energy of an ideal gas is the sum of total kinetic

energy of molecules only.

2 a) i) The r.m.s. speed of oxygen gas molecules is 500 m s-1

at certain

temperature and pressure. What would be the r.m.s. speed of hydrogen

gas molecules at the same temperature and pressure if the molar mass

of oxygen is 16 times that of hydrogen?

(ii) At what temperature will the r.m.s. speed of nitrogen gas molecules

equal to that of oxygen gas molecules at 300 K, if the relative

molecular masses of nitrogen and oxygen are 28 g mol-1

and 32 g mol-1

respectively.

(b) 2 g helium gas of molar mass 4 g mol-1

in a container has a temperature of 47 0C and a pressure of 1.20 X 10

5 Pa.

i) Calculate the internal energy of the gas and the number of helium gas

molecules.

(ii) 5 g neon gas of molar mass 20 g mol-1

and of temperature 47 0C is

added into the container at a constant volume. Find the new pressure

inside the container and the new value of the internal energy



3 a) The temperature of an ideal gas is increased from 100 0C to 200

0C while the

volume and the number of moles stay constant. Find the ratio

i) between the final pressure and the initial pressure of the gas molecules

ii) between the final r.m.s. speed and the initial r.m.s. speed of the gas

molecules

b) In the lungs, the respiratory membrane separates tiny sacs of air (absolute

pressure of 105 Pa) from the blood in the capillaries. These spherical sacs are

called alveoli, and it is from them that oxygen enters the blood. The average

radius of the alveoli is 0.125 mm, and the air inside each sac contains 14% of

oxygen. Assuming that the air behaves as an ideal gas at body temperature

(310 K), find the number of oxygen gas molecules in one of the sacs.

c) Determine the pressure of hydrogen gas if the gas contains 7.50 X 1017

molecules per unit volume and the r.m.s. speed of the gas molecules is 2.50

km s-1

. Given the molar mass of hydrogen is 2 g mol-1

.



15.0: THERMODYNAMIC

1 a) When a gas expands adiabatically, the internal energy of the gas increases.

Describe the situation of the gas by using first law of thermodynamics in order

to deny the statement.

b) A gas is confined to a rigid container that cannot expand when heat energy is

added to it. State the thermodynamic process for this situation.

FIGURE 1

c) Suppose a monatomic ideal gas is changed from state A to state D by the

processes shown on the PV diagram in FIGURE 1. Calculate the total work

done of the gas when the gas follows the constant-pressure path, followed by

the constant temperature path. [ ]



2 a) Define the following process.

i) Isothermal expansion.

ii) Isobaric compression.

b) Derive the expression of work done for an isobaric process.

c) State the first law of thermodynamic.

FIGURE 2

(d) FIGURE 2 shows a graph of an ideal gas which undergoes three

thermodynamic processes from initial state labelled 1, to its final state labelled

4. The pressure of the gas decreased by half in its first process and compressed

by half of its initial volume in its second isothermal process. Finally the

pressure of the gas is increased until it reaches twice of its initial pressure. If

initially the gas is at of temperature, 1atm and has 3 moles of atoms,

calculate:

i) its final temperature.

[6 marks]

ii) the total work done during the three processes.

Documents

FIGURE 1 - YSL Physics - Homeyslphysics.weebly.com/uploads/4/8/2/6/48261583/sep_sem_1.pdf · ... A boy rides a bicycle along a straight line from his house to a ... by the car when