Movimiento Circular, Momentun lineal y Energía

7/22/2019 Movimiento Circular, Momentun lineal y Energa

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3. A ball of mass m falls from rest on to a horizontal plate and bounces off it. The magnitudes of

its velocity just before and just after the bounce are v1

and v2

respectively. The variation with

time tof the velocity v of the ball is shown below.

v

v

v

00 t t t t

1

1 2 3

2

The magnitude of the net force on the ball is given by which one of the following?

A. 1

1

t

mv

B.)(

23

2

tt

mv

C.

( )

( )12

21

tt

vvm

D.

( )

( )12

21

tt

vvm

+

(1)

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4. Joe is standing on the surface of a frozen pond and he throws a ball horizontally. Considering

Joe and the ball together, which one of the following correctly describes the change in the

magnitude of the momentum and the change in the kinetic energy of Joe and the ball

immediately after the ball is thrown?

Magnitude of momentum of Joe and ball Kinetic energy of Joe and ball

A. No change Increases

B. Increases Increases

C. No change No change

D. Increases No change

(1)

5. An astronaut in outer space is holding a hammer and drifting at constant velocity. The astronaut

throws the hammer in the opposite direction to that in which she is drifting.

What change, if any, occurs in the total kinetic energy and the total momentum of the astronaut

and hammer?

Total kinetic energy Total momentum

A. unchanged increased

B. unchanged unchanged

C. increased increased

D. increased unchanged

(1)

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6. A constant force is applied to a ball of mass m. The velocity of the ball changes from v1

to v2.

The impulse received by the ball is

A. m(v2

+ v1).

B. m(v2 v1).

C. m(v2

2+ v

1

2).

D. m(v2

2v

1

2).

(1)

7. This question is about the collision between two railway trucks (carts).

(a) Define linear momentum.

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In the diagram below, railway truck A is moving along a horizontal track. It collides with a

stationary truck B and on collision, the two join together. Immediately before the collision, truck

A is moving with speed 5.0 ms1

. Immediately after collision, the speed of the trucks is v.

BA

5 . 0 m s 1

I m m e d i a t e l y b e f o r e c o l l i s i o n

I m m e d i a t e l y a f t e r c o l l i s i o n

BA

v

The mass of truck A is 800 kg and the mass of truck B is 1200 kg.

(b) (i) Calculate the speed v immediately after the collision.

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(ii) Calculate the total kinetic energy lost during the collision.

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(c) Suggest what has happened to the lost kinetic energy.

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(Total 8 marks)

8. A ball of mass 2.0 kg falls vertically and hits the ground with speed 7.0 ms1

as shown below.

7 . 0 m s 1

13 . 0 m s

before after

The ball leaves the ground with a vertical speed 3.0 ms1

.

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The magnitude of the change in momentum of the ball is

A. zero.

B. 8.0 Ns.

C. 10 Ns.

D. 20 Ns.(1)

9. Which of the following quantities are conserved in an inelastic collision in an isolated system of

two objects?

Linear momentum of system Kinetic energy of system

A. Yes Yes

B. Yes No

C. No Yes

D. No No

(1)

10. This question is about conservation of momentum and conservation of energy.

(a) State Newtons third law.

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(b) State the law of conservation of momentum.

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The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest

and ball A is moving with speed Valong a line joining the centres of the balls. The mass of each

ball isM.

A B

v

B e f o r e c o l l i s i o n

During the collision of the balls, the magnitude of the force that ball A exerts on ball B is FAB

and the magnitude of the force that ball B exerts on ball A isFBA

.

(c) On the diagram below, add labelled arrows to represent the magnitude and direction of

the forcesFAB

andFBA

.

A BD u r i n g t h e c o l l i s i o n

(3)

The balls are in contact for a time t. After the collision, the speed of ball A is +vA

and the speed

of ball B is +vB

in the directions shown.

A BA f t e r t h e c o l l i s i o n

v A v B

As a result of the collision, there is a change in momentum of ball A and of ball B.

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(d) Use Newtons second law of motion to deduce an expression relating the forces acting

during the collision to the change in momentum of

(i) ball B.

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

(ii) ball A.

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

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

(e) Apply Newtons third law and your answers to (d), to deduce that the change in

momentum of the system (ball A and ball B) as a result of this collision, is zero.

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(f) Deduce, that if kinetic energy is conserved in the collision, then after the collision, ball A

will come to rest and ball B will move with speed V.

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(Total 17 marks)

11. A stone on a string is moving in a circle as shown below.

P

Q

v

v

y d i r e c t i o n

x d i r e c t i o n

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At point P, the stone of mass m has speed v in they-direction. A quarter of a revolution later, the

stone at point Q has speed v in thex-direction.

What is the change, in they-direction only, of the magnitude of the momentum of the stone?

A. zero

B. mv

C. mv2

D. 2mv(1)

12. Two spheres X and Y are moving towards each other along the same straight line with momenta

of magnitudePX

andPY

respectively. The spheres collide and move off with momentapX

and

pY

respectively, as illustrated below.

X XY Y

P pP px xY Y

B e f o r e c o l l i s i o n A f t e r c o l l i s i o n

Which one of the following is a correct statement of the law of conservation of momentum for

this collision?

A. PX

+PY

=pX

+pY

B. PX

PY

=pX

+pY

C. PX

PY

=pX

pY

D. PX

+PY

=pX

pY

(1)

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13. This question is about driving a metal bar into the ground.

Large metal bars can be driven into the ground using a heavy falling object.

o b j e c t

m a s s = 2 . 0 1 0 k g3

b a rm a s s = 4 0 0 k g

In the situation shown, the object has a mass 2.0 103

kg and the metal bar has a mass of

400 kg.

The object strikes the bar at a speed of 6.0 m s1

. It comes to rest on the bar without bouncing.

As a result of the collision, the bar is driven into the ground to a depth of 0.75 m.

(a) Determine the speed of the bar immediately after the object strikes it.

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(b) Determine the average frictional force exerted by the ground on the bar.

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(Total 7 marks)

14. This question is about driving a metal bar into the ground and the engine used in the process.

Large metal bars can be driven into the ground using a heavy falling object.

o b j e c t m a s s = 2 . 0 1 0 k g

b a r m a s s = 4 0 0 k g

3

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In the situation shown, the object has a mass 2.0 103

kg and the metal bar has a mass of 400

kg.

The object strikes the bar at a speed of 6.0 m s1

It comes to rest on the bar without bouncing.

As a result of the collision, the bar is driven into the ground to a depth of 0.75 m.

(a) Determine the speed of the bar immediately after the object strikes it.

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(b) Determine the average frictional force exerted by the ground on the bar.

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(c) The object is raised by a diesel engine that has a useful power output of 7.2 kW.

In order that the falling object strikes the bar at a speed of 6.0 m s1

, it must be raised to a

certain height above the bar. Assuming that there are no energy losses due to friction,

calculate how long it takes the engine to raise the object to this height.

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The diagram below shows the relation between the pressure and the volume of the air in the

diesel engine for one cycle of operation of the engine. During the cycle there are two adiabatic

processes, an isochoric process and an isobaric process.

v o l u m e

p r e s s u r e

t h e r m a l e n e r g y

B C

D

A

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(d) Explain what is meant by

(i) an adiabatic process;

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(ii) an isochoric process;

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

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

(1)

(iii) an isobaric process.

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

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

(e) Identify, from the diagram, the following processes.

(i) Adiabatic processes

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

(ii) Isochoric process

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

(iii) Isobaric process

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

During the process B

C thermal energy is absorbed.

The diesel engine has a total power output of 8.4 kW and an efficiency of 40%. The cycle of

operation is repeated 40 times every second.

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(f) State what quantity is represented on the diagram by the area ABCD.

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

(g) Determine the value of the quantity that is represented by the area ABCD.

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(h) Determine the thermal energy absorbed during the process B C.

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(Total 22 marks)

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15. The momentum of a system is conserved if

A. no external forces act on the system.

B. no friction forces act within the system.

C. no kinetic energy is lost or gained by the system.

D. the forces acting on the system are in equilibrium.(1)

16. The velocity of a body of mass m changes by an amount v in a time t. The impulse given to

the body is equal to

A. mt.

B..

t

v

C..

t

vm

D. mv.

(1)

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17. A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface and

rebounds to a maximum height at point Y.

p o i n t X

p o i n t Y

b e f o r e a f t e r

Which one of the following graphs best shows the variation with time tof the momentump of

the ball as it moves between point X and point Y?

A . B .

C . D .

p

t0

0

p

t0

0

p

t0

0

p

t0

0

(1)

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18. A small ball P moves with speed v towards another identical ball Q along a line joining the

centres of the two balls. Ball Q is at rest. Kinetic energy is conserved in the collision.

P Q a t r e s t

v

Which one of the following situations is a possible outcome of the collision between the balls?

P Q

P Q

P Q

P Q

A . B .

C . D .

v v

v 3 v

44

v = 0v

v v

2 2

(1)

19. Two spheres of masses m1 and m2 are moving towards each other along the same straight-linewith speeds v

1and v

2as shown.

p o s i t i v e d i r e c t i o n

m 1 v 1 v 2 m 2

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. m1v

1+ m

2v

2

C. m1v

1 m

2v

2

D. m2v

2 m

1v

1

(1)

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(b) An ice hockey puck collides with the wall of an ice rink. The puck is sliding along a line

that makes an angle of 45 to the wall.

w a l l

i c e r i n k

d i r e c t i o n o f p u c kb e f o r e c o l l i s i o n

d i r e c t i o n o f p u c ka f t e c o l l i s i o nr

4 5 4 5

The collision between the wall and the puck is perfectly elastic.

(i) State what is meant by an elastic collision.

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(ii) Discuss how the law of conservation of momentum applies to this situation.

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(c) The diagram below is a scale diagram that shows the vector representing the momentum

of the puck before collision.

Scale: 1.0 cm = 0.10 N s

By adding appropriate vectors to the diagram, deduce that the magnitude of the change in

momentum of the puck as a result of the collision is 0.71 N s.(4)

(d) The sketch-graph below shows the variation with time tof the forceFexerted by the wall

on the puck.

F

00 t

The total contact time is 12 ms. Estimate, explaining your reasoning, the maximum force

exerted by the wall on the puck.

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(Total 12 marks)

22. The engine of a rocket ejects gas at high speed, as shown below.

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h i g h s p e e d

g a s

r o c k e t

d i r e c t i o n o f

m o t i o n o f r o c k e t

The rocket accelerates forwards because

A. the momentum of the gas is equal but opposite in direction to the momentum of the

rocket.

B. the gas pushes on the air at the back of the rocket.

C. the change in momentum of the gas gives rise to a force on the rocket.

D. the ejected gas creates a region of high pressure behind the rocket.

(1)

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23. A stationary metal plate is hanging freely on a string. A steel ball, travelling horizontally, hits

the plate. The speed of the ball after the collision is less than before, but still in a horizontal

direction, as shown below.

b e f o r e c o l l i s i o n

a f t e r c o l l i s i o n

s t r i n g

m e t a l p l a t e

Which one of the following gives a correct statement, with a valid reason, about the type of

collision between the ball and the plate?

Type of collision Reason

A. inelastic The sphere has changed its momentum during the collision.

B. inelastic The sphere has lost kinetic energy during the collision.

C. unknown The change in momentum of the plate during the collision is unknown.

D. unknown The kinetic energy of the plate after the collision is unknown.

(1)

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24. A fan and a sail are mounted vertically on a cart that is initially at rest on a horizontal table as

shown in the diagram below.

f a n a i r

s a i l

When the fan is turned on an air stream is blown towards the right and is incident on the sail.

The cart is free to move with negligible resistance forces.

After the fan has been turned on the cart will

A. move to the left and then to the right.

B. remain at rest.

C. move towards the right.

D. move towards the left.(1)

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25. Collisions

A large metal ball is hung from a crane by means of a cable of length 5.8 m as shown below.

In order to knock down a wall, the metal ball of mass 350 kg is pulled away from the wall and

then released. The crane does not move. The graph below shows the variation with time tof the

speed v of the ball after release.

v

/

m

s

1

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4

t / s

3 . 0

2 . 0

1 . 0

0 . 0

The ball makes contact with the wall when the cable from the crane is vertical.

(a) For the ball just before it hits the wall,

(i) state why the tension in the cable is not equal to the weight of the ball;

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

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(ii) by reference to the graph, estimate the tension in the cable. The acceleration of free

fall is 9.8 m s2

.

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(b) Use the graph to determine the distance moved by the ball after coming into contact with

the wall.

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(c) Calculate the total change in momentum of the ball during the collision of the ball with

the wall.

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(d) (i) State the law of conservation of momentum.

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(ii) The metal ball has lost momentum. Discuss whether the law applies to this

situation.

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(e) During the impact of the ball with the wall, 12% of the total kinetic energy of the ball is

converted into thermal energy in the ball. The metal of the ball has specific heat capacity

450 J kg1

K1

. Determine the average rise in temperature of the ball as a result of

colliding with the wall.

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(Total 16 marks)

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26. Collisions

A large metal ball is hung from a crane by means of a cable of length 5.8 m as shown below.

c r a n ec a b l e

5 . 8 m

w a l l

m e t a l b a l l

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In order to knock down a wall, the metal ball of mass 350 kg is pulled away from the wall and

then released. The crane does not move. The graph below shows the variation with time tof the

speed v of the ball after release.

v

/m

s

1

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4

t / s

3 . 0

2 . 0

1 . 0

0 . 0

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The ball makes contact with the wall when the cable from the crane is vertical.

(a) For the ball just before it hits the wall,

(i) state why the tension in the cable is not equal to the weight of the ball;

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

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

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(ii) by reference to the graph, estimate the tension in the cable. The acceleration of free

fall is 9.8 m s2

.

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(b) Use the graph to determine the distance moved by the ball after coming into contact with

the wall.

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(c) For the collision between the ball and the wall, calculate

(i) the total change in momentum of the ball;

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(ii) the average force exerted by the ball on the wall.

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(d) (i) State the law of conservation of momentum.

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(ii) The metal ball has lost momentum. Discuss whether the law applies to this

situation.

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(e) During the impact of the ball with the wall, 12% of the total kinetic energy of the ball is

converted into thermal energy in the ball. The metal of the ball has specific heat capacity

450 J kg1

K1

. Determine the average rise in temperature of the ball as a result of

colliding with the wall.

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(Total 18 marks)

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27. Two objects collide inelastically. For this system of two objects

A. only momentum is conserved.

B. only kinetic energy is conserved.

C. both momentum and kinetic energy are conserved.

D. neither momentum nor kinetic energy are conserved.(1)

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28. A net force of magnitudeFacts on a body for a time tproducing an impulse of magnitude Y.

Which of the following is the magnitude of the rate of change of momentum of the body?

A. F

B. Ft

C. Y

D. Yt

(1)

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29. This question is about Newtons laws of motion, the dynamics of a model helicopter and the

engine that powers it.

(a) Explain how Newtons third law leads to the concept of conservation of momentum in the

collision between two objects in an isolated system.

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(b) The diagram illustrates a model helicopter that is hovering in a stationary position.

r o t a t i n gb l a d e s

d o w n w a r d m o t i o n o f a i r

0 . 7 0 m0 . 7 0 m

The rotating blades of the helicopter force a column of air to move downwards. Explain

how this may enable the helicopter to remain stationary.

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(c) The length of each blade of the helicopter in (b) is 0.70 m. Deduce that the area that the

blades sweep out as they rotate is 1.5 m2. (Area of a circle = r

2)

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(d) For the hovering helicopter in (b), it is assumed that all the air beneath the blades is

pushed vertically downwards with the same speed of 4.0 m s1

. No other air is disturbed.

The density of the air is 1.2 kg m3

.

Calculate, for the air moved downwards by the rotating blades,

(i) the mass per second;

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(ii) the rate of change of momentum.

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(e) State the magnitude of the force that the air beneath the blades exerts on the blades.

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(f) Calculate the mass of the helicopter and its load.

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(g) In order to move forward, the helicopter blades are made to incline at an angle to the

horizontal as shown schematically below.

While moving forward, the helicopter does not move vertically up or down. In the space

provided below draw a free body force diagram that shows the forces acting on the

helicopter blades at the moment that the helicopter starts to move forward. On your

diagram, label the angle.

(4)

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(h) Use your diagram in (g) to explain why a forward forceFnow acts on the helicopter and

deduce that the initial acceleration a of the helicopter is given by

a =gtan

wheregis the acceleration of free fall.

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(i) The helicopter is driven by an engine that has a useful power output of 9.0 102 W. The

engine makes 300 revolutions per second. Deduce that the work done in one cycle is 3.0

J.

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(j) The diagram below shows the relation between the pressure and the volume of the air in

the engine for one cycle of operation of the engine.

A

B C

D

p r e s s u r e

v o l u m e

(i) State the name given to the type of process represented by DA.

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

(ii) During one cycle of the engine, the gas absorbs Q1 units of thermal energy and Q2units of thermal energy are transferred from the gas. On the diagram above, draw

labelled arrows to show these energy transfers.(2)

(iii) The efficiency of the engine is 60%. Using your answer to question (i), calculate

the values ofQ1

and Q2.

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(Total 30 marks)

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30. The diagram below shows a trolley of mass 4.0 kg moving on a frictionless horizontal table with

a speed of 2.0 m s1

. It collides with a stationary trolley also of mass 4.0 kg.

4 . 0 k g 4 . 0 k g

2 . 0 m s 1

Which of the following diagrams shows a possible outcome?

2 . 0 m s 1

2 . 0 m s 1

2 . 0 m s 10 . 0 m s 1

0 . 0 m s 1

0 . 0 m s 1

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

A . B .

C . D .

(1)

31. Momentum

(a) State the law of conservation of linear momentum.

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(b) A toy rocket of mass 0.12 kg contains 0.59 kg of water as shown in the diagram below.

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h i g h - p r e s s u r e a i r

n o z z l e , r a d i u s 1 . 4 m m

w a t e r

The space above the water contains high-pressure air. The nozzle of the rocket has a

circular cross-section of radius 1.4 mm. When the nozzle is opened, water emerges from

the nozzle at a constant speed of 18 m s1

. The density of water is 1000 kg m3

.

(i) Deduce that the volume of water ejected per second through the nozzle is 1.1 10

4 m3.

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

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(ii) Deduce that the upward force that the ejected water exerts on the rocket is

approximately 2.0 N. Explain your working by reference to Newtons laws of

motion.

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(iii) Calculate the time delay between opening the nozzle and the rocket achieving lift-

off.

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

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

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

(Total 10 marks)

32. Temperature, specific heat and latent heat

(a) Outline how a temperature scale is constructed.

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

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

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

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

(b) Discuss why even an accurate thermometer may affect the reliability of a temperaturereading.

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(c) (i) Definespecific heat capacity.

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

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

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

(ii) The table below gives data for water and ice.

specific heat capacity of water

specific latent heat of fusion of ice

4.2 kJ kg1

K1

330 kJ kg1

A beaker contains 450 g of water at a temperature of 24C. The thermal (heat)

capacity of the beaker is negligible and no heat is gained by, or lost to, theatmosphere. Calculate the mass of ice, initially at 0C, that must be mixed with the

water so that the final temperature of the contents of the beaker is 8.0C.

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Ideal gases and heat engines

(d) An ideal gas is contained in a cylinder by means of a piston as shown below.

i d e a l g a s

c y l i n d e r

p i s t o n

The piston is pushed quickly into the cylinder.

For the resulting change of state of the gas,

(i) state, and explain, whether the change is isochoric, isobaric or adiabatic.

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

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

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

(ii) use the molecular model of an ideal gas to explain why the temperature of the gas

changes.

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(e) A heat engine operates between a high-temperature source and a sink at a lower

temperature as shown below.

s o u r c e

e n g i n e

s i n k

6 8 0 J

W

The overall efficiency of the engine is 15%. The engine transfers 680 J of energy to the

sink.

(i) Determine the workWdone by the engine.

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

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

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

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

(ii) There is a gain in entropy as a result of the engine doing workW. Identify twofurther entropy changes and, by reference to the second law of thermodynamics,

state how the three changes are related.

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(Total 21 marks)

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33. A ball of massMhits a wall at speed Vnormal to the wall. It rebounds with speed v normal to

the wall as shown below.

w a l l

M

V

v

l e f t r i g h t

What is the magnitude of the change in momentum of the ball and the direction of the force that

the wall exerts on the ball?

change in momentum direction of force

A. M(Vv) to the right

B. M(Vv) to the left

C. M(V+ v) to the right

D. M(V+ v) to the left

(1)

34. A rocket is fired vertically into the air. When the rocket reaches its maximum height, the rocket

explodes.

What change, if any, occurs in the momentum and in the kinetic energy of the rocket during the

explosion?

momentum kinetic energy

A. increases increases

B. increases constantC. constant increases

D. constant constant

(1)

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35. This question is about momentum and energy.

(a) Define impulse of a force and state the relation between impulse and momentum.

definition:

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

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

relation:

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

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

(b) By applying Newtons laws of motion to the collision of two particles, deduce that

momentum is conserved in the collision.

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(c) In an experiment to measure the speed of a bullet, the bullet is fired into a piece of

plasticine suspended from a rigid support by a light thread.

2 4 c m

s p e e d Vb u l l e t

p l a s t i c i n e

The speed of the bullet on impact with the plasticine is V. As a result of the impact, the

bullet embeds itself in the plasticine and the plasticine is displaced vertically through a

height of 24 cm. The mass of the bullet is 5.2103

kg and the mass of the plasticine is

0.38 kg.

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(i) Ignoring the mass of the bullet, calculate the speed of the plasticine immediately

after the impact.

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

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

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

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

(ii) Deduce that the speed Vwith which the bullet strikes the plasticine is about

160 m s1

.

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

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

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

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

(Total 11 marks)

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36. This question is about momentum and energy.

(a) Define impulse of a force and state the relation between impulse and momentum.

definition

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

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

relation

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

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

(b) By applying Newtons laws of motion to the collision of two particles, deduce that

momentum is conserved in the collision.

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

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

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

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(c) In an experiment to measure the speed of a bullet, the bullet is fired into a piece of

plasticine suspended from a rigid support by a light thread.

2 4 c m

s p e e d Vb u l l e t

p l a s t i c i n e

The speed of the bullet on impact with the plasticine is V. As a result of the impact, the

bullet embeds itself in the plasticine and the plasticine is displaced vertically through a

height of 24 cm. The mass of the bullet is 5.2103

kg and the mass of the plasticine is

0.38 kg.

(i) Ignoring the mass of the bullet, calculate the speed of the plasticine immediately

after the impact.

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

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

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

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

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(ii) Deduce that the speed Vwith which the bullet strikes the plasticine is about

160 m s1

.

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

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

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

(iii) Estimate the kinetic energy lost in the impact.

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(d) Another bullet is fired from a different gun into a large block of wood. The block remains

stationary after impact and the bullet melts completely. The temperature rise of the block

is negligible. Use the data to estimate the minimum impact speed of the bullet.

mass of bullet = 5.3103

kg

specific heat capacity of the material of the bullet = 130 J kg

1

K

1

latent heat of fusion of the material of the bullet = 870 J kg1

melting point of the material of the bullet = 330C

initial temperature of bullet = 30C

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(Total 19 marks)

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37. Two trolleys P and Q, are connected by a rubber band. They are at rest on a horizontal surface.

The mass of Q is twice that of P. The trolleys are pulled apart so that the band is stretched and

are then released.

The ratioQtrolleyofonacceleratiinitialofmagnitude

Ptrolleyofonacceleratiinitialofmagnitude

is

A. 4

1

.

B. 2

1

.

C. 1.

D. 2.

(1)

38. An impulseIacts on a body of mass m that is initially at rest. What is the distance moved by the

body in a time tafter the impulse has been delivered?

A. m

It

B. t

Im

C. m

I

D. It(1)

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39. This question is about momentum.

(a) Define

(i) linear momentum.

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

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

(ii) impulse.

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

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

(b) In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed

of 18 m s1

. It passes through a shallow tank containing stationary water. The tank is of

length 9.3 m. The carriage leaves the tank at a speed of 13 m s1

.

1 8 m s

c a r r i a g e , m a s s 4 5 0 k g

9 . 3 m

w a t e r - t a n k 1 3 m s 1 1

As the carriage passes through the tank, the carriage loses momentum and causes some

water to be pushed forwards with a speed of 19 m s1

in the direction of motion of the

carriage.

(i) For the carriage passing through the water-tank, deduce that the magnitude of its

total change in momentum is 2250N s.

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(ii) Use the answer in (b)(i) to deduce that the mass of water moved in the direction of

motion of the carriage is approximately 120 kg.

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(iii) Calculate the mean value of the magnitude of the acceleration of the carriage in the

water.

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(c) For the carriage in (b) passing through the water-tank, determine

(i) its total loss in kinetic energy.

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(ii) the gain in kinetic energy of the water that is moved in the direction of motion of

the carriage.

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

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

(1)

(d) By reference to the principles of conservation of momentum and of energy, explain your

answers in (c).

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

(Total 15 marks)

40. This question is about linear motion.

A car moves along a straight road. At time t= 0 the car starts to move from rest and oil begins to

drip from the engine of the car. One drop of oil is produced every 0.80 s. Oil drops are left onthe road. The position of the oil drops are drawn to scale on the grid below such that 1.0 cm

represents 4.0 m. The grid starts at time t= 0.

d i r e c t i o n o f m o t i o n

1 . 0 c m

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(a) (i) State the feature of the diagram above which indicates that, initially, the car is

accelerating.

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

(ii) On the grid above, draw further dots to show where oil would have dripped if the

drops had been produced from the time when the car had started to move.(2)

(iii) Determine the distance moved by the car during the first 5.6 s of its motion.

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

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

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(b) Using information from the grid above, determine for the car,

(i) the final constant speed.

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

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

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

(ii) the initial acceleration.

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

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

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

(2)(Total 8 marks)

41. 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. m1v

1+ m

2v

2

C. m1v

1 m

2v

2

D. m2v

2 m

1v

1

(1)

42. Two satellites of equal mass, S1

and S2, orbit the Earth. S

1is orbiting at a distance rfrom the

Earths centre at speed v. S2

orbits at a distance 2rfrom the Earths centre at speed 2

v

. The

ratio of the centripetal force on S1

to the centripetal force on S2

is

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A. 8

1

.

B. 4

1

.

C. 4.

D. 8.(1)

43. A satellite orbits the Earth at constant speed as shown below.

E a r t h

s a t e l l i t e

(a) Draw on the diagram

(i) an arrow labelled F to show the direction of the gravitational force of the Earth on

the satellite.

(ii) an arrow labelled V to show the direction of the velocity of the satellite.(2)

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(b) Although the speed of the satellite is constant, it is accelerating. Explain why it is

accelerating.

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

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

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

(c) Discuss whether or not the gravitational force does work on the satellite.

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

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

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

(Total 7 marks)

44. This question is about a wind turbine.

Air of density and speed v passes normally through an areaA.

(a) Deduce that the kinetic energy of the air passing through the area per unit time is given by

the expression

kinetic energy per unit time =.

3

2

1 Av

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

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

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

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Air of constant density 1.2 kg m3

is incident at a speed of 9.0 m s1

on the blades of a wind

turbine. The turbine blades are each of length 7.5 m. The air passes through the turbine without

any change of direction. Immediately after passing through the blades, the speed of the air is 5.0

m s1

as illustrated below.

w i n d s p e e d w i n d s p e e d

9 . 0 m s 1

5 . 0 m s 1

t u r b i n e b l a d e s

The density of air immediately after passing through the blades is 2.2 kg m3

. The turbine and

generator have an overall efficiency of 72%

.

(b) Calculate

(i) the power extracted from the air by the turbine;

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

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

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

(ii) the electrical power generated.

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

(Total 5 marks)

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45. Which one of the following graphs best represents the variation of the kinetic energy, KE, and

of the gravitational potential energy, GPE, of an orbiting satellite with its distance rfrom the

centre of the Earth?

0

0

0

0

0

0

0

0

E n e r g y

E n e r g y

E n e r g y

E n e r g y

K E

K E

K E

K E

G P E

G P E

G P E

G P E

r

r

r

r

A .

C .

B .

D .

(1)

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46. A particle P is moving in a circle with uniform speed. Which one of the following diagrams

correctly shows the direction of the acceleration a and velocity v of the particle at one instant of

time?

A . B .

C . D .

a

aa

a

v

v

v

v

P P

P P

(1)

47. The centripetal force that causes a car to go round a bend in the road is provided by

A. the force produced by the car engine acting on the wheels.

B. the friction between the tyres and the road.

C. the weight of the car.

D. the force exerted by the driver on the steering wheel.(1)

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48. This question is about the kinematics and dynamics of circular motion.

(a) A car goes round a curve in a road at constant speed. Explain why, although its speed is

constant, it is accelerating.

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

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

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

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

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

In the diagram below, a marble (small glass sphere) rolls down a track, the bottom part of whichhas been bent into a loop. The end A of the track, from which the marble is released, is at a

height of 0.80 m above the ground. Point B is the lowest point and point C the highest point of

the loop. The diameter of the loop is 0.35 m.

A

m a r b l e

g r o u n d B

C0 . 8 0 m

0 . 3 5 m

The mass of the marble is 0.050 kg. Friction forces and any gain in kinetic energy due to the

rotating of the marble can be ignored. The acceleration due to gravity,g= 10 ms2

.

Consider the marble when it is at point C.

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(b) (i) On the diagram opposite, draw an arrow to show the direction of the resultant force

acting on the marble.(1)

(ii) State the names of the two forces acting on the marble.

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

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

(iii) Deduce that the speed of the marble is 3.0 ms1

.

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

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

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(iv) Determine the resultant force acting on the marble and hence determine the

reaction force of the track on the marble.

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Documents

Movimiento Circular, Momentun lineal y Energía