NJCTL



Momentum/Impulse

1. A pulley consists of two mass m1 and m2 where m1< m2 and the system moves with a velocity v. The total linear momentum of the system is

(A) (m1 + m2) v (B) (m2 - m1) v (C) ½(ml+m2)v (D) ½(m2 - m1)v (E) m2v

2. Two balls, each of mass m, have equal speeds v along paths inclined at 30° from the normal as shown above. If they collide and stick together their velocity after the collision has magnitude

(A) [pic]v (B) [pic] (C) [pic] (D) [pic] (E) v

3. An object having an initial momentum that may be represented by the vector above strikes an object that is initially at rest. Which of the following sets of vectors may represent the momenta of the two objects after the collision?

Questions 4-6

A block of mass m has a speed vo on a horizontal frictionless surface, as shown above. The block collides elastically with another block of mass m initially at rest. The second block collides and sticks to a third block of mass m initially at rest.

4. What is final speed of the first block?

(A) vo (B) vo/2 (C) 2 vo (D) 4 vo (E) 0

5. How fast is the second block moving after the first collision?

(A) vo (B) vo/2 (C) 2 vo (D) 4 vo (E) 0

6. What is the final speed of the two block system after the blocks stick together?

(A) vo (B) vo/2 (C) 2 vo (D) 4 vo (E) 0

7. Block m1 is moving with speed vo toward stationary block m2 collides and sticks with it. The speed of the center of mass of the system is

(A) [pic]vo (B) [pic] vo (C) [pic] vo (D) [pic] vo (E) [pic] vo

8. A cannonball of mass 2m is moving towards the right with initial velocity vo and explodes into two equal pieces each with mass m. What is the speed of the center of mass after the explosion?

(A) vo (B) 0.5 vo (C) 2 vo (D) 4 vo (E) 0

9. A bullet of mass M1 is fired from a gun that is initially at rest. The combined mass of the gun and bullet is M2. If after the bullet is fired its kinetic energy is Ke, what is the kinetic energy of the gun when it recoils?

(A) Ke (B) [pic] (C) [pic] D) [pic] (E) [pic]

10. A rubber ball is dropped from a building 10 meters tall onto the cement surface below so that when it hits the surface the collision can be assumed to be elastic. The motion of the ball is best described as

(A) simple harmonic with a period of about 1.4 s

(B) simple harmonic with a period of about 2.8 s

(C) simple harmonic with an amplitude of 5 m

(D) periodic with a period of about 2.8 s but not simple harmonic

(E) periodic with a period of about 1.4 s but not simple harmonic

Questions 11-13

An object explodes into three pieces of unequal mass. Two of the pieces that follow the paths with velocity v as shown above have a mass m. the third piece is known to have a mass of 2m.

11. What is the direction of the third piece of the object?

(A) (B) (C) (D) (E)

12. How fast is the third piece of the object?

(A) v/4 (B) v/2 (c) v (D) 2 v (E) 4 v

13. A ball of mass m is moving to the right with speed 3v on a frictionless tabletop when it collides with a second ball of mass 3m that is moving to the right with speed v. If the two balls stick together upon impact the speed of the balls immediately after the collision is

(A) v/3 (B) v/2 (C) 2v/3 (D) 3v/2 (E) 2v

14. Person A and Person B are standing on a sheet of frictionless ice. Person A pushes Person B so that Person B who is 60 kg, moves to the right at 3 m/s, while Person A, who is 55 kg, moves to the left at 2 m/s. What is the velocity of their center of mass?

(A) Zero (B) 0.5 m/s to the left (C) 1 m/s to the right (D) 2.4 m/s to the left (E) 2.5 m/s to the right

15. What is the rebound speed of a 2 kg ball falling straight down that hits the floor moving at 4 m/s, if the average normal force exerted by the floor on the ball was 80 N for 0.5s?

(A) 2 m/s (B) 11 m/s (C) 16 m/s (D) 19 m/s (E) 44 m/s

16. A 2 kg mass moving at 12 m/s collides with an identical mass moving at -8 m/s and the mass stick together. What is the final velocity of the two masses?

(A) 4/3 m/s (B) 2 m/s (C) 6 m/s (D) 10 m/s (E) 12 m/s

17. A compressed spring is placed between two masses M and m resting on a smooth horizontal surface. When the spring is released, the two fly apart with M moving at velocity V. The velocity of m is

(A) (M/m)V (B) (-M/m)V (C) (m/M)V (D) (-m/M)V (E) [(m)/(m+M)]V

18. Consider these two cases. First, a car moving at 40 mph hits another car of equal mass moving at 40 mph in the opposite direction. Second, a car moving at 40 mph hits a stationary steel wall.

The collision time is the same for the two cases and the collisions are both inelastic. In which of these cases would result in the greatest impact force?

(A) Hitting the wall (B) Hitting the other car (C) The force would be the same in both cases (D)More information is needed (E)None of the above are true.

Questions 19-20

A mass M moving with speed v collides with an uncompressed stationary spring of mass M with a spring constant K. The surface is frictionless.

19. What will be the maximum compression of the spring?

(A) v[pic] (B) v[pic] (C) [pic] [pic] (D) v[pic] (E) v[pic]

20. What is the speed of the spring after the collision?

(A) v (B) [pic] (C) [pic] (D) 2v (E) [pic]

Questions 21-22

A 6kg mass is moving at 12 m/s in the +x direction is acted upon by a force acting in the –x direction with magnitude given as a function of time by the graph.

[pic]

21. Find the magnitude of the change in momentum.

(A) 12 kg m/s (B) 24 kg m/s (C) 36 kg m/s (D) 40 kg m/s (E) 52 kg m/s

22. What is the velocity of the mass after the force has stopped acting?

(A)6 m/s (B) 10 m/s (C) 18 m/s (D) 24 m/s (E) 40 m/s

23. A wire is bent into the shape as shown above. Which of the following best represents the coordinates of the center of mass?

(A) (13/14, 6/7) (B) (8/7, 6/7) (C) (13/14, 8/7) (D) (1,1) (E) (1,6/7)

24. If only the resultant force acting on an object and the time during when the force acts on it are given, which of the following can be determined about the object?

(A) its impulse (B) its change in velocity (C) its change in kinetic energy (D) its mass (E) its acceleration

25. A block of mass m is moving with speed vi to the right on a frictionless surface when it explodes into two pieces of unequal mass. One piece of the mass, 3m/4 moves with a speed vi/2 to the left while the other piece of the object moves with velocity

(A) vi/2 (B) 2vi/3 (C) 11vi/2 (D) 7vi/5 (E) 2vi

Questions 26-27

26. A 5 kg box and a 10 kg box are connected by a rod of negligible mass. Which of the following points represents the center of mass of the box rod combination?

(A) A (B) B (C) C (D) D (E) E

27. The system is free to rotate about an axis that can be placed at any of the five points above. Which point should the axis be placed so the moment of inertia of the combination is at its greatest?

(A) A (B) B (C) C (D) D (E) E

28. The center of mass of a uniform wire, bent in the shape shown above, is located closest to point

(A) A (B) B (C) C (D) D (E) E

Questions 29-31

The graph above shows the force on a 5 kg object (5N per division) as a function of time (5s per division)

29. How fast is the object moving at t=0?

(A) 0 m/s (B) 5 m/s (C) 10 m/s (D) 15 m/s (E) 20 m/s

30. What is the acceleration of the object at t=4?

(A) 0 m/s2 (B) 1 m/s2 (C) 3 m/s2 (D) 5 m/s2 (E) 10 m/s2

31. What is the impulse of the system at t=4?

(A) 0 kg m/s (B) 5 kg m/s (C) 10 kg m/s (D) 15 kg m/s (E) 20 kg m/s

Questions 32-36

A bullet of mass m moving with velocity v shoots into a block of mass 3m initially at rest. The block moves on the frictionless plane until it collides elastically with another block of mass 4m initially at rest. The other block slides down the incline and is launched off the small cliff.

32. How fast does the bullet block system move after the first collision?

(A) v (B) [pic] (C) [pic] (D) 2v (E) [pic]

33. How fast does the other block move after the second collision?

(A) v (B) [pic] (C) [pic] (D) 2v (E) [pic]

34. How fast does the block move when it is launched off the ledge?

(A) [pic] (B) [pic] (C) [pic] (D) [pic] (E) 0

35. How far does the block travel away from the ledge?

(A)[pic] (B)[pic] (C) [pic] (D) H (E) 0

36. How does the kinetic energy of the block on the ground compare to the initial kinetic energy of the bullet?

(A) Less than (B) Equal to (C) Greater than (D) None (Ke=zero) (E) Cannot be determined

Problems 37 -38

37. A mass rebounds off a wall elastically as shown above. The vector that best represents the impulse delivered by the wall is

(A) (B) (C) (D) (E)

38. What is the change in momentum of the mass “m” after hits the wall?

(A) Mvsinθ (B)mvcosθ (C) 2mv (D) 2mvcosθ (E) 2mvsinθ

Answer Key:

|Question Number |Answer |

| | |

|1 |A |

|2 |D |

|3 |E |

|4 |E |

|5 |A |

|6 |B |

|7 |E |

|8 |A |

|9 |D |

|10 |D |

|11 |D |

|12 |B |

|13 |D |

|14 |A |

|15 |C |

|16 |B |

|17 |B |

|18 |B |

|19 |E |

|20 |A |

|21 |C |

|22 |C |

|23 |A |

|24 |A |

|25 |C |

|26 |B |

|27 |E |

|28 |B |

|29 |A |

|30 |B |

|31 |E |

|32 |C |

|33 |C |

|34 |B |

|35 |B |

|36 |C |

|37 |C |

|38 |D |

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m1

m2

30°

30°

(A)

(B)

(C)

(D)

(E)

m

m

m

vo

m

3m

3v

v

1

1

2

2

Y

X

m

vi

A

B

C

D

E

5kg

10kg

L

L

L

L/2

L/4

L/4

A

B

C

D

E

F

t

v

3m

3m

2H

H

v

v

[?]¬¬¬¬?pbθ

θ

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