momentum&collisions

7/26/2019 Momentum&Collisions

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Nombre:__________________________________

MOMENTUM & COLLISIONS

1. A rocket is fired vertically. At its highest point, it explodes. Which one of the following describes what

happens to its total momentum and total kinetic energy as a result of the explosion?

Total momentum Total kinetic energy

A. unchanged increased

B. unchanged unchanged

C. increased increased

D. increased unchanged

2. Which of the following quantities are conserved in an inelastic collision between two bodies?

Total linear momentum of the bodies Total kinetic energy of the bodies

A. Yes yes

B. yes no

C. no yes

D. no no

3. Joe is standing on the surface of a frozen pond and he throws a ball horizontally. Considering Joeand the ball together, which oneof the following correctly describes the change in the magnitude ofthe momentum and the change in the kinetic energy of Joe and the ball immediately after the ball isthrown?

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

4. 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.


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5. A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface andrebounds to a maximum height at point Y.

point X

point Y

before after

Which one of the following graphs best shows the variation with time tof the momentum pof the ballas it moves between point X and point Y?

A. B.

C. D.

p

t0

0

p

t0

0

p

t

0

0

p

t

0

0


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6. A small ball P moves with speed v towards another identical ball Q along a line joining the centres ofthe two balls. Ball Q is at rest. Kinetic energy is conserved in the collision.

P Q at rest

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 3v

44

v= 0 v

v v

2 2

7. Two spheres of masses m1 and m2 are moving towards each other along the same straight -line with

speeds v1 and v2 as shown.

positive direction

m 1 v1 v2 m2

The spheres collide. Which of the following gives the total change in linear momentum of the spheresas a result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 - m2v2

D. m2v2 - m1v1

8. An object of mass mis initially at rest. An impulse Iacts on the object. The change in kinetic energyof the object is

A. .2

2

m

I

B. .

2

m

I

C. I2m.

D. 2I2m.


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

high speed

gas

rocket

direction of

motion of rocket

The rocket accelerates forwards because

A. the momentum of the gasis 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.

10. 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, asshown below.

before collision

after collision

string

metal plate

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


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11. A fan and a sail are mounted vertically on a cart that is initially at rest on a horizontal table as shownin the diagram below.

fan air

sail

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

12. 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.

13. A net force of magnitude Facts on a body for a time tproducing an impulse of magnitude Y. Whichof the following is the magnitude of the rate of change of momentum of the body?

A. F

B. F t

C. Y

D. Y t

14. The diagram below shows a trolley of mass 4.0 kg moving on a frictionless horizontal table with aspeed of 2.0 m s

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

4.0kg 4.0kg

2.0ms1


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Which of the following diagrams shows a possible outcome?

2.0ms1

2.0ms1

2.0ms10.0ms1

0.0ms1

0.0ms1

4.0kg

4.0kg

4.0kg

4.0kg

4.0kg

4.0kg

4.0kg

4.0kg

A. B.

C. D.

15. A ball of mass Mhits a wall at speed Vnormal to the wall. It rebounds with speed vnormal to thewall as shown below.

wall

M

V

v

left right

What is the magnitude of the change in momentum of the ball and the direction of the force that thewall exerts on the ball?

change in momentum direction of force

A. M(V v) to the right

B. M(V v) to the leftC. M(V+ v) to the right

D. M(V+ v) to the left


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

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

Momentum kinetic energy

A. Increases increases

B. Increases constant

C. Constant increases

D. Constant constant

17. Two trolleys P and Q, are connected by a rubber band. They are at rest on a horizontal surface. Themass of Q is twice that of P. The trolleys are pulled apart so that the band is stretched and are thenreleased.

The ratioQtrolleyofonacceleratiinitialofmagnitude

Ptrolleyofonacceleratiinitialofmagnitudeis

A. 4

1.

B.2

1.

C. 1.

D. 2.

18. An impulse Iacts on a body of mass mthat is initially at rest. What is the distance moved by the bodyin a time tafter the impulse has been delivered?

A. m

It

B.t

Im

C. m

I

D. It

19. 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 spheresas a result of the collision?

A. 0


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B. m1v1 + m2v2

C. m1v1 - m2v2

D. m2v2 - m1v1

20. Momentum

(a) State the law of conservation of momentum.

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(b) An ice hockey puck collides with the wall of an ice rink. The puck is sliding along a line thatmakes an angle of 45 to the wall.

wall

ice rink

direction of puckbefore collision

direction of puckafte collisionr

45 45

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


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By adding appropriate vectors to the diagram, deduce that the magnitude of the change inmomentum of the puck as a result of the collision is 0.71 N s.

(d) The sketch-graph below shows the variation with time tof the force Fexerted by the wall onthe puck.

F

00 t

The total contact time is 12 ms. Estimate, explaining your reasoning, the maximum forceexerted by the wall on the puck.

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22. This question is about momentum.

(a) Define

(i) linear momentum.

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(ii) impulse.

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(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

.

18 m s

carriage, mass 450 kg

9.3m

water-tank 13 m s11

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 thecarriage.

(i) For the carriage passing through the water-tank, deduce that the magnitude of its totalchange in momentum is2250N s.

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

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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 thecarriage.

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(d) By reference to the principles of conservation of momentum and of energy, explain youranswers in (c).

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23. 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 dripfrom the engine of the car. One drop of oil is produced every 0.80 s. Oil drops are left on the 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.

direction of motion

1.0cm

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

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(ii) On the grid above, draw further dots to show where oil would have dripped if the dropshad been produced from the time when the car had started to move.

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

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

(i) the final constant speed.

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(ii) the initial acceleration.

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25. 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.

high-pressure air

nozzle, radius 1.4mm

water

The space above the water contains high-pressure air. The nozzle of the rocket has a circularcross-section of radius 1.4 mm. When the nozzle is opened, water emerges from the nozzle at

a constant speedof 18 m s1

. Thedensity of water is 1000 kg m3

.

(i) Deduce that the volume of water ejected per second through the nozzle is 1.1 104

m3

.

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

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momentum&collisions

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