40 - Nassau BOCES



MOMENTUM

PART A PROBLEMS

1. A 1.0-kilogram object falls freely from rest. The magnitude of its momentum after 1.0 second of fall is:

1) 1.0 kgm/s

2) 4.9-kgm/s

3) 9.8 kgm/s

4) 20. kgm/s

2. Which is a scalar quantity?

1) speed

2) displacement

3) force

4) momentum

3. A mass having a momentum of 40 kilogram( meters per second receive an impulse of 20 Newton(seconds in the direction of motion. The final momentum of the mass is:

1) 2.0 kg m/s

2) 20 kg m/s

3) 60 kg m/s

4) 800 kg m/s

4. A mass of 2.0 kilograms that experiences a momentum change of 50. kilogram(meters per second must have received an impulse of:

1) 25 N s

2) 2.0 N s

3) 50. N s

4) 100 Ns

5. A mass experiences a change of momentum of 35 kilogram ( meters per second in 10 seconds. What is the magnitude of the average force causing this change?

1) 3.5 N

2) 35 N

3) 45 N

4) 350 N

6. If a 2.0-kilogram mass moves with a constant speed of 20 meters per second, the magnitude of its momentum is:

1) 8.0-kg m/s

2) 10. kg m/s

3) 40. kg m/s

4) 160 kg m/s

7. A 1-kilogram ball of putty traveling at 5 meters per second hits a wall perpendicularly and sticks to it. The ball experiences a change of momentum of:

1) 1 kg m/s

2) 5 kg m/s

3) 10 kg m/s

4) 0 kg m/s

8. A 1-kilogram ball hits a surface perpendicularly with a speed of 3 meters per second and bounces back with a speed of 2 meters per second. The ball undergoes a change in momentum of:

1) 1 kg m/s

2) 5 kg m/s

3) 3 kg m/s

4) 6 kg m/s

9. An average unbalanced force of 30 Newton’s acts on a 2.0-kilogram object for 3.0 seconds. The object's change in momentum is:

1) 10. kg m/s

2) 15 kg m/s

3) 6.0 kg m/s

4) 90. kg m/s

10. As an object falls freely toward the earth, the momentum of the object earth system

1) decreases

2) increases

3) remains the same

11. As the momentum of a moving mass increases, the magnitude of the impulse required to stop the mass

1) decreases

2) increases

3) remains the same

12. As a freely falling object approaches the earth's surface, the impulse required to stop the object

1) increases

2) decreases

3) remains the same

13. An object traveling at 4.0 meters per second has a momentum of 16 kilogram-meters per second. What is the mass of the object?

1) 64 kg

2) 20 kg

3) 12 kg

4) 4.0 kg

QUESTIONS 14-17: A horizontal force is applied to a 5.0-kilogram object resting on a horizontal surface. The force is always applied in the same direction, but its magnitude varies with time according to the graph. (Neglect friction.)

14. What is the acceleration of the object at time t 2.5 seconds?

1) 1.0 m/s2

2) 0.20 m/s2

3) 5.0 m/s2

4) 9.8 m/s2

15. During which time interval did the object have a constant velocity?

1) 0.0 s to 1.0 s

2) 1.0 s to 2.0 s

3) 2.0 s to 3.0 s

4) 3.0 s to 4.0 s

16. The greatest change in momentum of the object occurred during the time interval from

1) 0.0 s to 1.0 s

2) 1.0s to 2.0 s

3) 2.0 s to 3.0 s

4) 3.0 s to 4.0 s

17. If a 5.0-kilogram mass is added to the original mass at the time t = 2.5 seconds, the acceleration of the object will:

1) decrease

2) increase

3) remain the same

18. A 15-newton force acts on an object in a direction due east for 3.0 seconds. What will be the change in. momentum of the object?

1) 45 kg-m/s due east

2) 45 kg-m/s due west

3) 5.0 kg-m/s due east

4) 0.20 kg-m/s due west

19. A 5.0-kilogram cart moving with a velocity of 4.0 meters per second is brought to a stop in 2.0 seconds. The magnitude of the average force used to stop the cart is:

1) 20. N

2) 2.0 N

3) 10. N

4) 4.0 N

20. A 5.0-newton force imparts an impulse of 15 newton-seconds to an object. The force acted on the object for a period of:

1) 0.33 s

2) 20. s

3) 3.0 s

4) 75 s

21. A net force of 12 newtons acting north on an object for 4.0 seconds will produce an impulse of:

1) 48 kg m/s north

2) 48 kg-m/s south

3) 3.0 kg-m/s north

4) 3.0 kg-m/s south

22. If a 3.0-kilogram object moves 10 meters in 2.0 seconds, its average momentum is:

1) 60. kg-m/s

2) 30. kg-m/s

3) 15 kg-m/s

4) 10. kg-m/s

23. An impulse of 30.0 Newton-seconds is applied to a 5.00-kilogram mass. If the mass had a speed of 100. meters per second before the impulse, its speed after the impulse could be:

1) 250. m/s

2) 106 m/s

3) 6.00 m/s

4) 0 m/s

24. The direction of an object's momentum is always the same as the direction of the object's:

1) inertia

2) potential energy

3) velocity

4) weight

25. An unbalanced force of 20 newtons is applied to an object for 10 seconds. The change in the momentum of the object will be:

1) 200 kg-m/s

2) 2,000 kg-m/s

3) 10,000 kg-m/s

4) 20,000 kg-m/s

26. An unfortunate bug strikes the windshield of a bus in a head-on collision. Which of the following statements are true?

1) The magnitude of the force encountered by the bug is greater than that of the bus

2) The magnitude of the impulse encountered by the bug is greater than that of the bus

3) The magnitude of the momentum change encountered by the bug is greater than that of the bus

4) The magnitude of the velocity change encountered by the bug is greater than that of the bus

5) The magnitude of the acceleration encountered by the bug is greater than that of the bus

27. A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If the impulse occurs for time duration of 0.01 s, then the average force (magnitude only) acting upon the ball is:

1) 0.14 N

2) 150 N

3) 350 N

4) 500 N

5) none of these

28. Padded dashboards in cars are safer in an accident than non-padded ones because they ____.

1) increase the impact time

2) decrease an occupant's impulse

3) decrease the impact force

4) two of the above

5) none of the above

29. A 4 kg ball has a momentum of 12 kg(m/s. The ball's speed is ___ m/s.

1) 3

2) 4

3) 12

4) 48

5) none of these

30. A 10-kilogram mass moving at a speed of 5.0 meters per second on a frictionless surface collides with a stationary 10-kilogram mass. If the two masses remain joined after the collision, their speed will be

1) 0.0 m/s

2) 2.5 m/s

3) 5.0 m/s

4) 10. m/s

31. A 10-kilogram gun recoils with a speed of 0.1 meter per second as it fires a 0.001-kilogram bullet. Neglecting friction, what is the speed of the bullet as it leaves the gun?

1) 10 m/s

2) 100 m/s

3) 1,000 m/s

4) 10,000 m/s

32. When two stationary objects are suddenly pushed apart by a compressed spring between them, and no friction acts on the objects, the total momentum of the system:

1) increases

2) decreases

3) remains the same

QUESTIONS 33-36: Block A moves with a velocity of 2 meters per second to the right and then collides with block B, which is at rest. After the collision, block A stops moving, and block B moves to the right.

33. What is the magnitude of the combined momentum of blocks A and B before the collision?

1) 0 kg m/s

2) 10 kg m/s

3) 20 kg m/s

4) 40 kg m/s

34. What is the total change in momentum of blocks A and B during the collision?

1) 0 kg m/s

2) 20 kg m/s

3) 40 kg m/s

4) 200 kg m/s

35. If block A is stopped in 0.1 second, the magnitude of the average force acting on block A is:

1) 50 N

2) 100 N

3) 200 N

4) 400 N

36. If the blocks had remained together after collision, the magnitude of their velocity would have been:

1) 1 m/s

2) 2 m/s

3) 0 m/s

4) 0.5 m/s

37. Two carts resting on a frictionless surface are forced apart by a spring. One cart has a mass of 2 kilograms and moves to the left at a speed of 3 meters per second. If the second cart has a mass of 3 kilograms, it will move to the right at a speed of:

1) 1 m/s

2) 2 m/s

3) 3 m/s

4) 6 m/s

38. Two carts of masses of 5.0 kilograms and 1.0 kilogram are pushed apart by a compressed spring. If the 5.0-kilogram cart moves westward at 2.0 meters per second, the magnitude of the velocity of the 1.0-kilogram cart will be

1) 2.0 kg-m/s

2) 2.0 m/s

3) 10. kg-m/s

4) 10. m/s

39. Two disk magnets are arranged at rest on a frictionless horizontal surface as shown in the diagram. When the string holding them together is cut, they move apart under a magnetic force of repulsion. When the 1.0-kilogram disk reaches a speed of 3.0 meters per second, what is the speed of the 0.5-kilogram disk?

1) 1.0 m/s

2) 0.50 m/s

3) 3.0 m/s

4) 6.0m/s

40. The diagram represents two identical carts, attached by a cord moving to the right at speed V. If the cord is cut, what would be the speed of cart A?

1) 0

2) 2V

3) V

4) V/2

41. A 4.0-kilogram mass is moving at 3.0 meters per second toward the right and a 6.0-kilogram mass is moving at 2.0 meters per second toward the left on a horizontal frictionless table. If the two masses collide and remain together after the collision, their final momentum is:

1) 1.0 kg-m/s

2) 24 kg-m/s

3) 12 kg-m/s

4) 0 kg-m/s

42. 2-kilogram car and a 3-kilogram car are originally at rest on a horizontal, frictionless surface as shown in the diagram below. A compressed spring is released, causing the cars to separate. The 3-kilogram car reaches a maximum speed of 2 meters per second. What is the maximum speed of the 2-kilogram car?

1) 1 m/s

2) 2 m/s

3) 3 m/s

4) 6 m/s

43. A 2.0-kilogram cart traveling east with a speed of 6 meters per second collides with a 3.0-kilogram cart traveling west. If both carts come to rest immediately after the collision, what was the speed of the westbound cart before the collision?

1) 6 m/s

2) 2 m/s

3) 3 m/s

4) 4 m/s

44. Two carts resting on a frictionless surface are forced apart by a spring. One cart has a mass of 6 kilograms and moves to the left at a speed of 3 meters per second. If the second cart has a mass of 9 kilograms, it will move to the right at a speed of:

1) 1 m/s

2) 2 m/s

3) 3 m/s

4) 6 m/s

45. A 2.0-kilogram rifle initially at rest fires a 0.002-kilogram bullet. As the bullet leaves the rifle with a velocity of 500 meters per second, what is the momentum of the rifle-bullet system?

1) 2.5 kg(m/s

2) 2.0 kg(m/s

3) 0.5 kg(m/s

4) 0 kg(m/s

46. A 4.0-kilogram mass is moving at 3.0 meters per second toward the right, and a 6.0-kilogram mass is moving at 2.0 meters per second toward the left, on a horizontal, frictionless table. If the two masses collide and remain together after the collision, their final momentum is:

1) 1.0 kg m/s

2) 24 kg m/s

3) 12 kg m/s

4) 0 kg m/s

47. At the circus, a 100.-kilogram clown is fired at 15 meters per second from a 500.-kilogram cannon. What is the recoil speed of the cannon?

1) 75 m/s

2) 15 m/s

3) 3.0 m/s

4) 5.0 m/s

48. Two carts are pushed apart by an expanding spring, as shown in the diagram below. If the average force on the 1-kilogram cart is 1 newton, what is the average force on the 2-kilogram cart?

1) 1 N

2) 0.0 N

3) 0.5 N

4) 4 N

49. In the diagram below, a 60-kilogram roller skater exerts a 10-newton force on a 30. -Kilogram roller skater for 0.20 second. What is the magnitude of the impulse applied to the 30. -Kilogram roller skater?

1) 50. N•s

2) 2.0 N•s

3) 6.0 N•s

4) 12 N•s

PART B PROBLEMS

1. A 2-kg cart moving to the right at 5 m/s collides with an 8-kg cart at rest. As a result of the collision, the carts lock together. What is the velocity of the carts after the collision? ______m/s. [1]

2. A standard physics problem is the "explosion" of two carts initially at rest, which sends them moving in opposite directions. For example the diagram below shows a 6-kg cart and a 4-kg cart at rest. Between them is a compressed spring. When the spring expands it sends both cars in opposite directions. If the 6kg cart moves to the left with a velocity of 6m/s, what is the velocity of the other cart?

3. A woman, driving a golf ball off a tee, gives the ball a velocity of +28m/s. The mass of the golf ball is .045kg, and the duration of the impact with the golf club is 6 x 10-3 seconds.

a. What is the change in momentum of the golf ball? _____m/s. [1]

b. What is the impulse imparted to the ball by the club? ______ N(s. [1]

4. A 55-kg swimmer is standing on a stationary 210 kg-floating raft. The swimmer funs off the raft horizontally with a velocity of 4.6 m/s. Find the recoil velocity of the raft. _____ m/s. [1]

5. A 1550kg car, traveling with a velocity of 12m/s plows into the back of a 1,000kg stationary car. During the collision the two cars lock bumpers and move off together as a unit. What velocity do they move off at? [2]

6. A 31kg skateboarder runs horizontally with a speed of 4m/s onto the stationary 5kg skateboard. Find the velocity of the two after the collision. _____ m/s. [1]

7. A 0.80-kg ball strikes a wall moving at 5.0 m/s and rebounds in the opposite direction at 3.5 m/s. If the collision with the wall endures for a total time of 0.0080 s, the average force acting upon the ball is _______N. [1]

 

8. A 16.0-kg ball is thrown with a speed of 22.0 m/s to a 55-kg clown who is at rest on ice. The clown catches the ball and glides across the ice. The velocity of the clown (and ball) immediately following the catch is ______m/s. [1]

 

9. A 16.0-kg ball is thrown with a speed of 22.0 m/s to a 55-kg clown on ice. At the time that the clown catches the ball, she is moving with a speed of 3.0 m/s in the same direction as the ball. The clown catches the ball and continues to glide across the ice. The velocity of the clown (and ball) immediately following the catch is ________ m/s. [2]

10. A 0.050-kg billiard ball moving at 1.2 m/s strikes a second 0.050-kg billiard ball which is moving in the same direction with a speed of 0.40 m/s. If the faster ball slows down to a speed of 0.65 m/s, then the speed of the second ball is ________m/s. [2]

 

11. A 0.050-kg billiard ball moving at 1.5 m/s strikes a second 0.050-kg billiard ball which is at rest on the table. If the first ball slows down to a speed of 0.10 m/s, the speed of the second ball is _____m/s. [1]

 

12. A 70-kg hockey player moving at 5.6 m/s collides head-on with an 80-kg player who is heading in the opposite direction with a speed of 3.5 m/s. The two players entangle and move together across the ice. Their after-collision speed is ______m/s. [2]

13. A terrified 70 kg Shawn accelerates from rest at a rate of 3m/s2 for 10 seconds after seeing a gigantic ghoul on Halloween night. What is his final momentum?

PART C PROBLEMS

1. During a goal-line stand, a 75-kg fullback moving eastward with a speed of 8 m/s collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s. The two players collide and stick together, moving at the same velocity after the collision. Determine the post-collision velocity of the two players. (CAREFUL: Be cautious of the +/- sign on the velocity of the two players.) [2]

2. A 15-kg medicine ball is thrown at a velocity of 20 km/hr to a 60-kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision. [2]

3. The brakes exert a 6.4 x 102 N force on a car weighing 15,680 Newton’s and moving at 20 m/s. The car finally stops:

a. What is the car’s mass

b. What is its initial momentum

c. What is the change in the cars momentum?

d. How long does the breaking force act on the car to bring it to a stop?

4. A .144 kg baseball is pitched horizontally at 38m/s. After it hits the bat it moves horizontally at 38m/s.

a. What impulse did the bat deliver to the ball?

b. If the ball and bat were in contact for .8ms, what was the average force exerted on the ball?

c. What was the average acceleration?

5. A car initially traveling at 23 m/s accelerates at 3m/s2 for 65 seconds:

a. What is its initial momentum

b. What is its final momentum

c. What is its change in momentum?

6. A 1500kg car initially moving with a speed of 15m/s collides head on with a utility pole and is brought

to rest in .3 seconds.

a. What is its initial momentum?

b. What is its final momentum?

c. What is the average force exerted on the car?

d. What is the change in momentum of the car?

e. What impulse was imparted to the car?

QUESTIONS 7-8: An 8.00 kilogram ball is fired horizontally from a 1.00×103 kilogram cannon initially at rest. After having been fired, the momentum of the ball is 2.40×103 kilogram•meters per second east. [Neglect friction.]

7. Calculate the magnitude of the cannon’s velocity after the ball is fired. [Show all work, including the equation and substitution with units.] [2]

8. Identify the direction of the cannon’s velocity after the ball is fired. [1]

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