IB Mechanics review questions 2014 - WikispacesMechanics+review... · IB Questionbank Physics 1 IB...

IB Questionbank Physics 1

IB Mechanics review questions 2014

2.1 Motion

1. 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)


2. 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)


3. 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)


5. 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)

6. Which of the following quantities can be determined from a speed-time graph of a particle travelling in a straight line?

A. Only the magnitude of the acceleration at a given instant

B. Both the velocity and the acceleration at a given instant

C. Only the distance travelled in a given time

D. Both the distance travelled in a given time and the magnitude of the acceleration at a given instant

(Total 1 mark)


7. 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)

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

A. Displacement

B. Distance

C. Power

D. Force (Total 1 mark)


9. 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)


10. 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)


11. 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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...................................................................................................................................... (1)

(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)


12. 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.



13. 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)


14. 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.



15. 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)


16. 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)


17. 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)


18. The graph below shows the variation with time t of the velocity v of an object moving on a straight-line.

Which of the graphs below best represents the variation with time t of the acceleration a of the object?

(Total 1 mark)

2.2 Forces

19. 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.

D. 4000 N. (Total 1 mark)


20. 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.


21. 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)

22. 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)


23. 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)

24. 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.



25. A cart of mass M is on a horizontal frictionless table.

The cart is connected to an object of weight W via a pulley. Which of the following is the acceleration of the cart?

A. W

g

WM

B.

g

WM

W

C. W

Mg

D. 0 (Total 1 mark)


26. Two steel balls, of mass M and 2M, fall at constant speeds in a tube filled with oil.

Which of the following correctly compares the magnitudes of the net force and of the drag (resistance) force on the two balls?

Net force Drag force

A. same same

B. same different

C. different same

D. different different

(Total 1 mark)

27. 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)


28. 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)

29. 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)


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

(a) Distinguish between average speed and instantaneous speed.

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(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.

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(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.

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

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(Total 11 marks)

31. A student is sitting on a chair. One force that is acting on the student is the pull of gravity. According to Newton’s third law, there must be another force which is

A. the upward push of the chair on the student.

B. the downward force on the student.

C. the downward push of the chair on Earth.

D. the upward force on Earth. (Total 1 mark)

32. 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)

33. If a moving object is subject to a constant force, which of the following can be correctly deduced from Newton’s first law?

A. The object continues to move with a changing velocity.

B. The object continues to move with a constant velocity.

C. The object continues to move with a changing direction.

D. The object continues to move in the same direction. (Total 1 mark)


34. 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)

35. 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)


36. A spacecraft orbits Earth. An astronaut inside the spacecraft feels “weightless” because

A. the gravitational field in the spacecraft is negligible.

B. the Earth exerts equal forces on the spacecraft and the astronaut.

C. the spacecraft and the astronaut have the same acceleration towards the Earth.

D. the spacecraft and the astronaut exert equal and opposite forces on each other. (Total 1 mark)

2.3 Work, Energy and Power

37. 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)

38. 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 %.

D. 60 %. (Total 1 mark)


39. 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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...................................................................................................................................... (1)

(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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40. Which of the following is equivalent to the principle of energy conservation?

A. Newton’s first law

B. The first law of thermodynamics

C. Newton’s second law

D. The second law of thermodynamics (Total 1 mark)

42. 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)


43. 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)


45. 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)

46. 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)


47. Which of the following is a correct definition of work?

A. Product of force and distance

B. Product of force and distance moved in the direction of the force

C. Product of power and time

D. Product of force and displacement (Total 1 mark)


49. 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)

50. 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)


51. 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)


52. 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)

53. 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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(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

.

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(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.

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(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.

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(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).

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(Total 16 marks)


54. 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)


57. 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)

58. 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)


59. 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.

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(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.

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(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.

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

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

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(Total 12 marks)


60. 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)

61. Mechanical power

(a) Define power.

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(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.

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(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

1.2 104 N.

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

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

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(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.

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(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.

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

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(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)

62. The variation with time of the vertical speed of a ball falling in air is shown below.

During the time from 0 to T, the ball gains kinetic energy and loses gravitational potential

energy Ep. Which of the following statements is true?

A. Ep is equal to the gain in kinetic energy.

B. Ep is greater than the gain in kinetic energy.

C. Ep is equal to the work done against air resistance.

D. Ep is less than the work done against air resistance.

(Total 1 mark)


2.4 Momentum and Impulse

64. 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)

65. A force F is applied to a body moving along a straight line. A resistive force f acts on the body. Both forces act along the same straight line as the motion of the body. The rate of change of momentum of the body is equal to

A. F – f.

B. F.

C. F + f.

D. f. (Total 1 mark)


66. 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)

67. 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)


68. 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.

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

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

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

(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.

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

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

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

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

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


(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

.

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

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

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

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

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

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

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

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

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

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


(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.

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

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

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

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

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

(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.

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

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

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

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

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

(Total 15 marks)


69. 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)


70. 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)




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

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

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


(not to scale)







4.8 m s–1

.

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

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

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

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



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

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

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

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

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

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

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

(c) The experiment is repeated with the clay block placed at the edge of the table so that it is

fired away from the table. The initial speed of the clay block is 4.3 m s–1

horizontally. The table surface is 0.85 m above the ground.

(not to scale)


(i) Ignoring air resistance, calculate the horizontal distance travelled by the clay block before it strikes the ground.

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

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

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

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

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

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

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

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

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

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

(ii) The diagram in (c) shows the path of the clay block neglecting air resistance. On the diagram, draw the approximate shape of the path that the clay block will take assuming that air resistance acts on the clay block.

(3)

(Total 15 marks)


72. 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)

73. 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.

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

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

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


(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.

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

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

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

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

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

(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

.

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

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

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


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

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

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

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

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

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

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

(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.

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

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

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

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

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

(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.

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

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

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

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

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

(Total 15 marks)


74. 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)

75. 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)


76. 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.

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

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


(ii) average power delivered to the bullet.

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

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

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

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

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

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

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

(Total 15 marks)


78. 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)

79. This question is about forces.

A solid iron ball of mass 770 kg is used on a building site. The ball is suspended by a rope from a crane. The distance from the point of suspension to the centre of mass of the ball is 12 m.

(a) Calculate the tension in the rope when the ball hangs vertical and stationary.

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

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


(b) The ball is pulled back from the vertical and then released. It falls through a vertical height of 1.6 m and strikes a wall.

(i) Calculate the speed of the ball just before impact.

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

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

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

(ii) Calculate the tension in the rope just before impact.

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

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

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


(c) The ball is brought to rest in 0.15 s. The sketch graph below shows how the force the ball exerts on the wall varies with time.

(i) State what quantity is represented by the area under the graph.

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

(ii) Determine the maximum force Fmax exerted by the ball on the wall.

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

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

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

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

(Total 10 marks)


80. 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)

81. 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)

82. 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)


Projectiles

83. A stone is thrown from a cliff and it lands in the sea as shown below. Air resistance is negligible.

Which of the following statements is correct whilst the stone is in motion?

A. The vertical component of the stone’s displacement is constant.

B. The horizontal component of the stone’s displacement is constant.

C. The vertical component of the stone’s velocity is constant.

D. The horizontal component of the stone’s velocity is constant. (Total 1 mark)


84. This question is about projectile motion.

A sphere is projected horizontally. The sphere is photographed at intervals of 0.10 s. The images of the sphere are shown against a grid on the diagram. Air resistance is negligible.


(a) Use data from the diagram to determine the acceleration of free fall.

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

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

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

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

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

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

(b) Determine the speed of the sphere 1.2 s after release.

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

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

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

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

(c) On the grid, draw the path of the sphere assuming air resistance is not negligible. (2)

(Total 10 marks)


85. The diagram shows the path of a projectile that is launched with velocity v. Air resistance is negligible.

A second projectile has double the mass of the first projectile and is launched with the same velocity. Air resistance is still negligible. Which of the following paths best represents the path of the projectile? (The original path is shown as a dotted line)

(Total 1 mark)



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

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

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



(not to scale)







4.8 m s–1

.

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

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

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

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



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

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

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

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

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

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

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

(c) The experiment is repeated with the clay block placed at the edge of the table so that it is

fired away from the table. The initial speed of the clay block is 4.3 m s–1

horizontally. The table surface is 0.85 m above the ground.

(not to scale)


(i) Ignoring air resistance, calculate the horizontal distance travelled by the clay block before it strikes the ground.

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

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

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

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

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

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

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

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

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

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

(ii) The diagram in (c) shows the path of the clay block neglecting air resistance. On the diagram, draw the approximate shape of the path that the clay block will take assuming that air resistance acts on the clay block.

(3)

(Total 15 marks)


87. An object moves in the x-y plane. The graphs below show how the component of its velocity Vx

in the x-direction and the component of its velocity Vy in the y-direction, vary with time t.

The particle is moving

A. in a parabola.

B. with simple harmonic motion.

C. with constant velocity in a straight line.

D. in a circle. (Total 1 mark)


88. A stone is thrown horizontally from the top of a cliff with an initial speed v.

The time of flight of the stone is t and its range R. Air resistance is negligible.

For a stone that is thrown horizontally from the top of the cliff with an initial speed 3v, which of the following is correct?

Time of flight Range

A. t R

B. 3t 3R

C. t 3R

D. 3t R

(Total 1 mark)


89. A football is kicked with an initial velocity u at an angle θ to the horizontal and reaches the ground t seconds later.

Ignoring air resistance what is the range R of the football?

A. ut

B. ut cos θ

C. ut sin θ

D. ut tan θ (Total 1 mark)

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