Worksheet 01 Mechanics

1 Worksheet (AS Mechanics)

AS and A Level Physics Imran Mirza (MSC Physics, PGCC Scotland, UK) 1

1 Worksheet (AS) Mechanics

Questions 2 and 3 refer to the following information.

A tractor of mass 1000 kg pulls a trailer of mass 1000 kg. The total resistance to motion

has a constant value of 4000 N. One quarter of this resistance acts on the trailer. At first,

the acceleration of the tractor and trailer is 2 m s-2

but eventually they move at a

constant speed of 6 m s-1

.

1. When the acceleration is 2 m s-2

, the force exerted on the tractor by the tow-bar is

A 1000 N B 2000 N C 3000 N D 5000 N

2. When the tractor and trailer are moving at constant speed of 6 m s-1

, the force exerted on

the tractor by the tow-bar is

A 0 N B 1000 N C 3000 N D 4000 N

3. A stone is thrown from P and follows a parabolic path. The highest point reached is T.

The vertical component of acceleration of the stone

A. is zero at T.

B. is greatest at T.

C. is greatest at P.

D. is the same at P as at T.

4. A steel sphere is held just below the surface of a deep tank of water and released. Which

one of the following best illustrates the relationship between the acceleration a, and the

displacement z, of the sphere? {Take g as 10 m s-2

]



5. The graph below shows how the force F exerted on a body in a collision with another

body varies with time t.

The area under the graph represents the body’s change of

A acceleration

B kinetic energy

C momentum

D potential energy

6. A neutron moving with an initial velocity u has a head-on elastic collision with a

stationary proton. After the collision, the velocity of the neutron is v and that of the

proton is w. Taking the masses of the neutron and proton to be equal, which one of the

following statements is wrong?

A. Conservation of momentum shows that u = v + w.

B. Conservation of energy shows that u2 = v

2 + w

2.

C. The momentum and energy equations taken together imply that the speed of the

proton after the collision is the same as that of the neutron before the collision.

D. The fact that the collision is elastic implies that the proton and the neutron move off

in opposite directions with equal speeds.

7. A body is moving with constant speed in the y-direction. For positive values of y, it

experiences a uniform acceleration in the x-direction. Which one of the paths A to E

does it follow?



8. An object falls vertically at its terminal velocity through air and then strikes soft ground

in which it becomes embedded. Its deceleration during impact is constant. If P

represents the point of impact, which one of the following graphs best represents the

variation of the total force R on the stone with distance s?

9. A man is parachuting at constant speed towards the surface of the Earth. The force

which, according to Newton’s third law, makes an action-reaction pair with the

gravitational force on the man is

A. the tension in the harness of the parachute.

B. the viscous force of the man and his parachute on the air.

C. the gravitational force on the Earth due to the man.

D. the viscous force of the air on the man and his parachute.

10. The velocity of a car which is decelerating uniformly changes from 30 m s

-1 to 15 m s

-1

in 75 m. After what further distance will it come to rest?

A 25 m B 37.5 m C 50 m D 75 m

11. An aeroplane, flying in a straight line at a constant height of 500 m with a speed of 200

m s-1

, drops an object. The object takes a time t to reach the ground and travels a

horizontal distance d in doing so. Taking g as 10 m s-2

and ignoring air resistance, which

one of the following gives the values of t and d?

t

d

A

25s

10 km

B

25s

5 km

C

10s

5 km

D

10s

2 km



12. Which one of the following pairs is not a valid example of action and reaction to which

Newton’s third law of motion applies?

A. the centripetal force holding a satellite in orbit round the Earth and the weight of the

satellite

B. the forces of repulsion experienced by each of two parallel wires carrying currents in

opposite directions

C. the forces of attraction felt by each of two gas molecules passing near to each other

D. the forces of attraction between an electron and a proton in a hydrogen atom

13. A particle X (of mass 4 units) and a particle Y (of mass 2 units) move directly towards

each other, collide and then separate. If ΔvX is the change of velocity of X and ΔvY is the

change of velocity of Y, what is the magnitude of the ratio ΔvX/ΔvY?

A ½ B 1/ 2 C 1 D 2

14. A mass is projected vertically upwards with a given velocity. Neglecting air resistance,

which one of the following statements is correct?

A. The kinetic energy of the mass is a maximum at the maximum height attained.

B. In accordance with the principle of conservation of energy, the total energy of the

mass is constant throughout the motion.

C. In accordance with the principle of conservation of momentum, the momentum of

the mass is constant throughout the motion.

D. The mass travels equal distances during equal periods of time during both ascent and

descent.

15. A parachutist of mass 80 kg descends vertically at a constant velocity of 3.0 m s-1

.

Taking the acceleration of free fall as 10 m s-2

, what it the net force acting on him?

A. 800 N upwards

B. zero

C. 240 N downwards

D. 360 N downwards

16. The force on a glass window in a vacuum system is 2 x 102 N when the pressure within

the system is 1 Pa and the atmospheric pressure is 1 x 105 Pa. If the pressure in the

system were reduced to 1 x 10-5

Pa, what would be the force on the window?

A 2 x 10-3

N B 1 x 102 N C 2 x 10

2 N D 4 x 10

2 N

17. Which one of the following statements is correct with reference to elastic collisions

between two bodies?

A. Momentum and total energy are conserved but kinetic energy may be changed into

some other form of energy.

B. Kinetic energy and total energy are both conserved but momentum is conserved only

if the two bodies have equal masses.

C. Kinetic energy is conserved; total momentum may decrease but cannot increase.

D. Momentum, kinetic energy and total energy are all conserved



18. A small metal sphere is released from rest at a height of a few centimeters above the

surface of a viscous liquid. On entering the liquid, the sphere experiences a viscous drag

proportional to its velocity. Which one of the following graphs most closely represents

the variation of acceleration a with time t for the sphere?

19. A student makes measurements from which he calculates the speed of sound as 327.66

m s-1

. He estimates that his result is accurate only to ±3%. Which one of the following

gives his result reduced to the appropriate number of significant figures?

A 300 m s-1

B 327 m s-1

C 330 m s-1

D 328 m s-1

20. A ball, dropped on to a 45o inclined plane, makes an elastic collision with the surface.

Stroboscopic photographs (a series of exposures on the same film at equal time

intervals) are taken of the path of the ball. Which one of the following diagrams best

represents the photographs?



1. The sketch graph below describes the motion of a ball rebounding from a horizontal

surface after being released from a point above the surface.

The quantity represented on the y-axis

is the ball’s

A. displacement.

B. velocity

C. acceleration

D. momentum

E. kinetic energy

2. In the diagram below, a body S of weight W hangs vertically by a thread tied at Q to the

string PQR.

If the system is in equilibrium,

what is the tension in the section PQ?

A. W tan 60o

B. W cos 60o

C. W tan 30o

D. W cos 30o

3. The velocity of a car which is decelerating

uniformly changes from 30 m s-1

to 15 m s-1

in 75 m. After what further distance will it come

to rest?

A 25 m B 37.5 m C 50 m D 75 m

4. The acceleration of free fall is determined by timing the fall of a steel ball

photoelectrically as shown below. The ball passes P and Q at times t1 and t2 after release.

What is the acceleration of free fall?

A. 2h / (t2 - t1)

B. h / (t22 - t1

2)

C. h2 / (t2 - t1)

D. 2h / (t22 - t1

2)



5. Two bodies P and Q, of equal mass, travelling towards one another on a level

frictionless track at speeds u and v respectively, make an elastic collision.

At some instant during the collision P is brought momentarily to rest. What is the speed

of Q at that instant?

A. zero

B. v - u

C. 2 (v - u)

D. ½ (v - u)

6. Forces of 4 N and 6 N act at a point. Which one of the following could not be the

magnitude of their resultant?

A. 1 N

B. 4 N

C. 6 N

D. 8 N

7. A trailer of weight 30 kN is hitched to a cab at the point X as shown in the diagram

below.

If the trailer carries a weight of 20 kN at the position shown in the diagram, what

upward force is exerted by the cab on the trailer at the point X?

A. 15 kN

B. 20 kN

C. 30 kN

D. 40 kN

8. A positron, a positively-charged particle of mass 10-30

kg, is moving at a speed v, which

is much less than the speed of light. It makes a head-on elastic collision with a stationary

proton of mass 10-27

kg. Which one of the following correctly describes the outcome of

the collision?

A. The positron comes to rest and the proton moves on at speed v.

B. The positron rebounds at speed v and the proton moves on at speed v.

C. The positron rebounds at a speed v/2 and the proton moves on at speed v/2.

D. The positron rebounds at a speed nearly equal to v, and the proton moves on at a

speed much less than v.



9. A mass is projected vertically upwards with a given velocity. Neglecting air resistance,

which one of the following statements is correct?

A. The kinetic energy of the mass is a maximum at the maximum height attained.

B. In accordance with the principle of conservation of energy, the total energy of the

mass is constant throughout the motion.

C. In accordance with the principle of conservation of momentum, the momentum of

the mass is constant throughout the motion.

D. The mass travels equal distances during equal periods of time during both ascent and

descent.

10. The diagram below shows a heavy flagpole PQ hinged at a vertical wall at end P and

held by a wire connected between end Q and a point R on

the wall. The weight of the flagpole is W and the tension in

the wire is T.

What is the direction of the force exerted by the wall on the

flagpole?

A. PQ B. PS

C. PX D. QP

11. An object of mass m passes a point X with a velocity v and slides up a frictionless

incline to stop at point Y which is at a height h above X.

A second object of mass ½ m passes X with a velocity of ½ v. To what height will it

rise?

A 41 h

B ½ h

C 2

1 h

D h

12. An electric motor is required to haul a cage of mass 400 kg up a mine shaft through a

vertical height of 1200 m in 2.0 minutes. What will be the electrical power required if

the overall efficiency is 80%. [Take g as 10 m s-2

]

A. 3.2 kW B. 5.0 kW C. 32 kW D. 50 kW

13. In order to support a load W, four light hinged rods P, Q, R and S are connected as

shown below and mounted in a vertical plane.

Which rods are in compression and which in tension?

in compression

in tension

A

P

Q, R ,S

B

P, Q

R, S

C

Q, R

P, S

D

Q, R ,S

P



14. A lunar landing module is descending to the Moon’s surface at a steady velocity of

10 m s-1

. At a height of 120 m, a small object falls from its landing gear.

Taking the Moon’s gravitational acceleration as 1.6 m s-2

, at what speed does the object

strike the Moon?

A 30 m s-1

B 22 m s-1

C 20 m s-1

D 17 m s-1

15. The diagram shows two trolleys X and Y about to collide. The momentum of each

trolley before the impact is given.

After the collision, the trolleys travel in opposite directions and the momentum of X is 2

kg m s-1

. What is the magnitude of the momentum of trolley Y?

A. 6 kg m s-1

B. 8 kg m s-1

C. 10 kg m s-1

D. 30 kg m s-1

16. What is the power required to give a body of mass m a forward acceleration a when it is

moving with velocity v up a frictionless track inclined at an angle θ to the horizontal?

A. mavg sinθ

B. mav sin θ + mgv

C. mav + mgv sin θ

D. (mav + mgv) sin θ

E. (mav + mgv)/sin θ

17. Two forces P and Q act at point X as shown in the vector diagram below.

In which of the following diagrams does the vector F represent the force which must be

applied at X to maintain equilibrium?



18. A constant force is applied to a body which is initially stationary but free to move in the

direction of the force. Assuming that the effects of friction are negligible, which of the

following graphs best represents the variation of P, the power supplied, with time t?

19. A stone thrown vertically upwards from ground level, rises to a height h and then falls

back to its starting point.

Assuming that air resistance is negligible, which of the following graphs best shows

how Ek, the kinetic energy of the stone, varies with s, the distance traveled?

20. A constant mass undergoes uniform acceleration when the resultant force acting on it

A is proportional to the displacement from a fixed point.

B is proportional to the velocity.

C is zero.

D is constant but not zero.

Worksheet 01 Mechanics

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