Chapter 9 Center of Mass and Linear Momentum Exam Prep

Chapter: Chapter 9

Learning Objectives

LO 9.1.0 Solve problems related to center of mass

LO 9.1.1 Given the positions of several particles along an axis or a plane, determine the location of their center of mass.

LO 9.1.2 Locate the center of mass of an extended, symmetric object by using the symmetry.

LO 9.1.3 For a two-dimensional or three-dimensional extended object with a uniform distribution of mass, determine the center of mass by (a) mentally dividing the object into simple geometric figures, each of which can be replaced by a particle at its center and (b) finding the center of mass of those particles.

LO 9.2.0 Solve problems related to Newton's second law for a system of particles

LO 9.2.1 Apply Newton’s second law to a system of particles by relating the net force (of the forces acting on the particles) to the acceleration of the system’s center of mass.

LO 9.2.2 Apply the constant-acceleration equations to the motion of the individual particles in a system and to the motion of the system’s center of mass.

LO 9.2.3 Given the mass and velocity of the particles in a system, calculate the velocity of the system’s center of mass.

LO 9.2.4 Given the mass and acceleration of the particles in a system, calculate the acceleration of the system’s center of mass.

LO 9.2.5 Given the position of a system’s center of mass as a function of time, determine the velocity of the center of mass.

LO 9.2.6 Given the velocity of a system’s center of mass as a function of time, determine the acceleration of the center of mass.

LO 9.2.7 Calculate the change in the velocity of a com by integrating the com’s acceleration function with respect to time.

LO 9.2.8 Calculate a com’s displacement by integrating the com’s velocity function with respect to time.

LO 9.2.9 When the particles in a two-particle system move without the system’s com moving, relate the displacements of the particles and the velocities of the particles.

LO 9.3.0 Solve problems related to linear momentum

LO 9.3.1 Identify that momentum is a vector quantity and thus has both magnitude and direction and also components.

LO 9.3.2 Calculate the (linear) momentum of a particle as the product of the particle’s mass and velocity.

LO 9.3.3 Calculate the change in momentum (magnitude and direction) when a particle changes its speed and direction of travel.

LO 9.3.4 Apply the relationship between a particle’s momentum and the (net) force acting on the particle.

LO 9.3.5 Calculate the momentum of a system of particles as the product of the system’s total mass and its center-of-mass velocity.

LO 9.3.6 Apply the relationship between a system’s center-of-mass momentum and the net force acting on the system.

LO 9.4.0 Solve problems related to collision and impulse

LO 9.4.1 Identify that impulse is a vector quantity and thus has both magnitude and direction and also components.

LO 9.4.2 Apply the relationship between impulse and momentum change.

LO 9.4.3 Apply the relationship between impulse, average force, and the time interval taken by the impulse.

LO 9.4.4 Apply the constant-acceleration equations to relate impulse to average force.

LO 9.4.5 Given force as a function of time, calculate the impulse (and thus also the momentum change) by integrating the function.

LO 9.4.6 Given a graph of force versus time, calculate the impulse (and thus also the momentum change) by graphical integration.

LO 9.4.7 In a continuous series of collisions by projectiles, calculate the average force on the target by relating it to the rate at which mass collides and to the velocity change experienced by each projectile.

LO 9.5.0 Solve problems related to conservation of linear momentum

LO 9.5.1 For an isolated system of particles, apply the conservation of linear momenta to relate the initial momenta of the particles to their momenta at a later instant.

LO 9.5.2 Identify that the conservation of linear momentum can be done along an individual axis by using components along that axis, provided that there is no net external force component along that axis.

LO 9.6.0 Solve problems related to momentum and kinetic energy in collisions

LO 9.6.1 Distinguish between elastic collisions, inelastic collisions, and completely inelastic collisions.

LO 9.6.2 Identify a one-dimensional collision as one where the objects move along a single axis, both before and after the collision.

LO 9.6.3 Apply the conservation of momentum for an isolated one-dimensional collision to relate the initial momenta of the objects to their momenta after the collision.

LO 9.6.4 Identify that in an isolated system, the momentum and velocity of the center of mass are not changed even if the objects collide.

LO 9.7.0 Solve problems related to elastic collisions in one dimension

LO 9.7.1 For isolated elastic collisions in one dimension, apply the conservation laws for both the total energy and the net momentum of the colliding bodies to relate the initial values to the values after the collision.

LO 9.7.2 For a projectile hitting a stationary target, identify the resulting motion for the three general cases: equal masses, target more massive than projectile, projectile more massive than target.

LO 9.8.0 Solve problems related to collisions in two dimensions

LO 9.8.1 For an isolated system in which a two-dimensional collision occurs, apply the conservation of momentum along each axis of a coordinate system to relate the momentum components along an axis before the collision to the momentum components along the same axis after the collision.

LO 9.8.2 For an isolated system in which a two-dimensional elastic collision occurs, (a) apply the conservation of momentum along each axis of a coordinate system to relate the momentum components along an axis before the collision to the momentum components along the same axis after the collision and (b) apply the conservation of total kinetic energy to relate the kinetic energies before and after the collision.

LO 9.9.0 Solve problems related to systems with varying mass: a rocket

LO 9.9.1 Apply the first rocket equation to relate the rate at which the rocket loses mass, the speed of the exhaust products relative to the rocket, the mass of the rocket, and the acceleration of the rocket.

LO 9.9.2 Apply the second rocket equation to relate the change in the rocket’s speed to the relative speed of the exhaust products and the initial and final mass of the rocket.

LO 9.9.3 For a moving system undergoing a change in mass at a given rate, relate that rate to the change in momentum.

Multiple Choice

1. Which one of the following statements is true?

A) the center of mass of an object must lie within the object

B) all the mass of an object is actually concentrated at its center of mass

C) the center of mass of an object cannot move if there is zero net force on the object

D) the center of mass of a cylinder must lie on its axis

E) none of the above

Difficulty: E

Section: 9-1

Learning Objective 9.1.1

2. The x and y coordinates in meters of the center of mass of the three-particle system shown below are:

A) 0 m, 0 m

B) 1.3 m, 1.7 m

C) 1.4 m, 1.9 m

D) 1.9 m, 2.5 m

E) 1.4 m, 2.5 m

Difficulty: E

Section: 9-1

Learning Objective 9.1.1

3. The center of mass of a uniform disk of radius R is located:

A) on the rim

B) a distance R/2 from the center

C) a distance R/3 from the center

D) a distance 2R/3 from the center

E) at the center

Difficulty: E

Section: 9-1

Learning Objective 9.1.1

4. The center of mass of the system consisting of Earth, the Sun, and the planet Mars is:

A) closer to the Earth than to either of the other bodies

B) closer to the Sun than to either of the other bodies

C) closer to Mars than to either of the other bodies

D) at the geometric center of the triangle formed by the three bodies

E) at the center of the line joining the Earth and Mars

Difficulty: E

Section: 9-1

Learning Objective 9.1.1

5. The center of mass of Earth's atmosphere is:

A) a little less than halfway between the Earth's surface and the outer boundary of the atmosphere

B) near the surface of the Earth

C) near the outer boundary of the atmosphere

D) near the center of the Earth

E) none of the above

Difficulty: E

Section: 9-1

Learning Objective 9.1.1

6. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass each other without colliding. At the end of 2.0 s the height above Earth's surface of the center of mass of the two-ball system is:

A) 2.9 m

B) 4.0 m

C) 7.1 m

D) 7.9 m

E) 10.4 m

Difficulty: M

Section: 9-1

Learning Objective 9.1.1

7. A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20 m apart, on frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move:

A) 1.0 m

B) 3.3 m

C) 10 m

D) 12 m

E) 17 m

Difficulty: M

Section: 9-1

Learning Objective 9.1.1

8. Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?

A) 4 m

B) 5 m

C) 6 m

D) 10 m

E) need to know the forces they exert

Difficulty: M

Section: 9-1

Learning Objective 9.1.1

9. A thick uniform wire is bent into the shape of the letter "U" as shown. Which point indicates the location of the center of mass of this wire?

A) A

B) B

C) C

D) D

E) E

Difficulty: E

Section: 9-1

Learning Objective 9.1.2

10. A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third. Rank the three plates according to the x coordinates of their centers of mass, from smallest to largest.

A) 1, 2, 3

B) 1 and 2 tie, then 3

C) 1, then 2 and 3 tie

D) 3, 2, 1

E) 1, 3, 2

Difficulty: E

Section: 9-1

Learning Objective 9.1.3

11. The center of mass of a system of particles has a constant velocity if:

A) the forces exerted by the particles on each other sum to zero

B) the external forces acting on particles of the system sum to zero

C) the velocity of the center of mass is initially zero

D) the particles are distributed symmetrically around the center of mass

E) the center of mass is at the geometric center of the system

Difficulty: E

Section: 9-2

Learning Objective 9.2.1

12. The center of mass of a system of particles remains at the same place if:

A) it is initially at rest and the external forces sum to zero

B) it is initially at rest and the internal forces sum to zero

C) the sum of the external forces is less than the maximum force of static friction

D) no friction acts internally

E) none of the above

Difficulty: E

Section: 9-2

Learning Objective 9.2.1

13. A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits there. Afterwards the canoe:

A) is forward of its original position and moving forward

B) is forward of its original position and moving backward

C) is rearward of its original position and moving forward

D) is rearward of its original position and moving backward

E) is rearward of its original position and not moving

Difficulty: E

Section: 9-2

Learning Objective 9.2.0

14. The center of mass of a system of particles obeys an equation similar to Newton's second law where:

A) is the total internal force and m is the total mass of the system

B) is the total internal force and m is the mass acting on the system

C) is the total external force and m is the total mass of the system

D) is the force of gravity and m is the mass of Earth

E) is the force of gravity and m is the total mass of the system

Difficulty: E

Section: 9-2

Learning Objective 9.2.1

15. A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest, the heavier object moves downward, and the lighter object moves upward with an acceleration of the same magnitude. Which of the following statements is true for the system consisting of the two objects?

A) The center of mass remains at rest.

B) The net external force is zero.

C) The velocity of the center of mass is a constant.

D) The acceleration of the center of mass is g, downward.

E) None of the above statements are true.

Difficulty: E

Section: 9-2

Learning Objective 9.2.1

16. Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35 m/s, 45 above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground?

A) 1.2 m

B) 20 m

C) 31 m

D) Can't tell because the velocities of the fragments are not given.

E) Can't tell because the coordinates of the highest point are not given.

Difficulty: M

Section: 9-2

Learning Objective 9.2.2

17. Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The center of mass of the two-block system is moving with the velocity of:

A) 1.3 m/s in the same direction as A

B) 1.3 m/s in the same direction as B

C) 2.7 m/s in the same direction as A

D) 1.0 m/s in the same direction as B

E) 5.0 m/s in the same direction as A

Difficulty: E

Section: 9-2

Learning Objective 9.2.3

18. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of the center of mass of the two-ball system is:

A) 11 m/s, down

B) 11 m/s, up

C) 15 m/s, down

D) 15 m/s, up

E) 20 m/s, down

Difficulty: M

Section: 9-2

Learning Objective 9.2.3

19. A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30 m/s. Since the only forces on the blocks are the force of gravity, the normal force of the surface, and the force of the spring, we conclude that:

A) the spring is compressed at the time of the observation

B) the spring is not compressed at the time of observation

C) the motion was started with the masses at rest

D) the motion was started with at least one of masses moving

E) the motion was started by compressing the spring

Difficulty: M

Section: 9-2

Learning Objective 9.2.3

20. At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the acceleration of the center of mass of the two-ball system is:

A) 0.25 g

B) 0.50 g

C) 0.67 g

D) 0.75 g

E) 1.0 g

Difficulty: E

Section: 9-2

Learning Objective 9.2.4

21. The position of the center of mass of a system of particles moves as x = 4.5 t + 2.4 t² + 1.1 t³, where x is in meters. If the system starts from rest at t = 0, what is its velocity at t = 3.0 s?

A) 8.0 m/s

B) 21 m/s

C) 49 m/s

D) 64 m/s

E) 65 m/s

Difficulty: E

Section: 9-2

Learning Objective 9.2.5

22. The velocity of the center of mass of a system of particles changes as v = 4.5 t + 2.4 t² + 1.1 t³, where v is in meters per second. If the system starts from rest at t = 0, what is its acceleration at t = 3.0 s?

A) 7.1 m/s²

B) 14 m/s²

C) 20 m/s²

D) 49 m/s²

E) 65 m/s²

Difficulty: E

Section: 9-2

Learning Objective 9.2.6

23. The acceleration of the center of mass of a system of particles changes as a = 4.5t + 2.4t² + 1.1t³, where a is in m/s². If the system starts from rest at t = 0, what is its velocity at t = 2.0 s?

A) 8.0 m/s

B) 14 m/s

C) 20 m/s

D) 27 m/s

E) 34 m/s

Difficulty: M

Section: 9-2

Learning Objective 9.2.7

24. The velocity of the center of mass of a system of particles changes as v = 4.5 t + 2.4 t² + 1.1 t³, where v is in meters per second. If the system starts from rest at t = 0, what is its position at t = 3.0 s?

A) 7.1 m

B) 21 m

C) 40 m

D) 49 m

E) 64 m

Difficulty: M

Section: 9-2

Learning Objective 9.2.8

25. A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:

A) 3.0 m/s left

B) 3.0 m/s, right

C) 6.0 m/s, right

D) 6.0 m/s, left

E) 17 m/s, right

Difficulty: E

Section: 9-2

Learning Objective 9.2.9

26. A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg mass is attached to the other end. The masses are placed on a horizontal surface and the spring is compressed 10 cm. The spring is then released with the masses at rest and the masses oscillate. When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s. The mechanical energy that has been lost to this instant is:

A) 0 J

B) 0.31 J

C) 0.61 J

D) 0.81 J

E) 1.2 J

Difficulty: M

Section: 9-2

Learning Objective 9.2.9

27. Momentum may be expressed in:

A) kg/m

B) grams

C) Ns

D) kg/(ms)

E) N/s

Difficulty: E

Section: 9-3

Learning Objective 9.3.0

28. The momentum of an object at a given instant is in the same direction as its:

A) displacement

B) velocity

C) acceleration

D) force

E) Momentum is a scalar and does not have a direction.

Difficulty: E

Section: 9-3

Learning Objective 9.3.1

29. The momentum of an object at a given instant is independent of its:

A) inertia

B) mass

C) speed

D) velocity

E) acceleration

Difficulty: E

Section: 9-3

Learning Objective 9.3.2

30. Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:

A) 1:9

B) 1:3

C) 1:1

D) 3:1

E) 9:1

Difficulty: E

Section: 9-3

Learning Objective 9.3.2

31. Two objects, P and Q, have the same momentum. Q can have more kinetic energy than P if it:

A) weighs more than P

B) is moving faster than P

C) weighs the same as P

D) is moving slower than P

E) is moving at the same speed as P

Difficulty: E

Section: 9-3

Learning Objective 9.3.2

32. A 2.5-kg stone is released from rest and falls toward Earth. After 4.0 s, the magnitude of its momentum is:

A) 98 kg∙m/s

B) 78 kg∙m/s

C) 39 kg∙m/s

D) 24 kg∙m/s

E) 0 kg∙m/s

Difficulty: M

Section: 9-3

Learning Objective 9.3.2

33. A 1.0 kg-ball moving at 2.0 m/s perpendicular to a wall rebounds from the wall at 1.5 m/s. The change in the momentum of the ball is:

A) zero

B) 0.5 N∙s away from wall

C) 0.5 N∙s toward wall

D) 3.5 N∙s away from wall

E) 3.5 N∙s toward wall

Difficulty: E

Section: 9-3

Learning Objective 9.3.3

34. A ball hits a wall and rebounds with the same speed, as diagrammed below. The changes in the components of the momentum of the ball are:

A) p_x > 0, p_y > 0

B) p_x < 0, p_y > 0

C) p_x = 0, p_y > 0

D) p_x = 0, p_y < 0

E) p_x > 0, p_y < 0

Difficulty: E

Section: 9-3

Learning Objective 9.3.3

35. A particle moves along the x axis. Its momentum is graphed below as a function of time. Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest.

A) 1, 2, 3, 4

B) 2, 3, 4, 1

C) 1, 4, 3, 2

D) 4, 3, 2, 1

E) 2, 4, 3, 1

Difficulty: E

Section: 9-3

Learning Objective 9.3.4

36. If the total momentum of a system is changing:

A) particles of the system must be exerting forces on each other

B) the system must be under the influence of gravity

C) the center of mass must have constant velocity

D) a net external force must be acting on the system

E) none of the above

Difficulty: E

Section: 9-3

Learning Objective 9.3.4

37. When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:

A) the force of your foot on the accelerator

B) the force of friction of the road on the tires

C) the force of the engine on the drive shaft

D) the normal force of the road on the tires

E) none of the above

Difficulty: E

Section: 9-3

Learning Objective 9.3.4

38. For a two-body collision, involving objects with different masses, a frame of reference which has the same velocity relative to the laboratory as does the center of mass of the two objects is:

A) a frame for which the momentum of the incident object is zero

B) a frame for which the momentum of the target object is zero

C) a frame for which the average momentum of the two objects is zero

D) a frame for which the total momentum of the two objects is zero

E) none of the above

Difficulty: E

Section: 9-3

Learning Objective 9.3.0

39. Force:

A) equals the negative integral (with respect to distance) of the potential energy function

B) is the ability to do work

C) is the rate of change of doing work

D) equals the time rate of change of momentum

E) has dimensions of momentum multiplied by time

Difficulty: E

Section: 9-3

Learning Objective 9.3.4

40. Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The momentum of the center of mass of the two-block system is:

A) 16 m/s in the same direction as A

B) 16 m/s in the same direction as B

C) 32 m/s in the same direction as A

D) 12 m/s in the same direction as B

E) 60 m/s in the same direction as A

Difficulty: M

Section: 9.3

Learning Objective 9.3.5

41. The acceleration of the center of mass of a system of particles:

A) depends on all the forces on all the particles

B) depends on all the velocities of all the particles

C) depends only on the forces external to the system of particles

D) depends only on the forces internal to the system of particles

E) depends only on the force of gravity

Difficulty: E

Section: 9.3

Learning Objective 9.3.6

42. The momentum of a system of particles is changing at the rate of 0.71 t + 1.2 t², in kg∙m/s. The net force at t = 2.0 s

A) cannot be determined without knowing the masses of the particles.

B) is 5.5 N

C) is 3.1 N

D) is 1.9 N

E) cannot be determined without knowing the momentum at t = 0

Difficulty: E

Section: 9.3

Learning Objective 9.3.6

43. The direction of the impulse on a struck baseball

A) depends on how fast the ball was thrown

B) is in the direction of the ball’s change in velocity

C) is in the direction of the force of gravity

D) depends on how hard the ball is struck

E) Impulse is a scalar, and does not have a direction associated with it.

Difficulty: E

Section: 9-4

Learning Objective 9.4.1

44. A 5-kg object can move along the x axis. It is subjected to a force in the positive x direction; a graph of F as a function of time t is shown below. Over the time the force is applied the change in the velocity of the object is:

A) 0.8 m/s

B) 1.3 m/s

C) 1.6 m/s

D) 2.3 m/s

E) 4.0 m/s

Difficulty: M

Section: 9-4

Learning Objective 9.4.2

45. The physical quantity "impulse" has the same dimensions as that of:

A) force

B) power

C) energy

D) momentum

E) work

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

46. A 0.3 kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds up at 20 m/s. The magnitude of the impulse due to the collision with the sidewalk is:

A) 3.0 N∙s

B) 6.0 N∙s

C) 9.0 N∙s

D) 15 N∙s

E) 29 N∙s

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

47. A 10-kg block of ice is at rest on a frictionless horizontal surface. A 1.0-N force is applied in an easterly direction for 1.0 s. During this time interval, the block:

A) acquires a speed of 1 m/s

B) moves 10 cm

C) acquires a momentum of 1.0 kg  m/s

D) acquires a kinetic energy of 0.1 J

E) none of the above

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

48. A uniform narrow bar, resting on frictionless ice, is given a transverse horizontal impulse at one end as shown. The center of mass of the bar COM will then:

A) remain at rest

B) move in a circle

C) move in a straight line

D) move in a parabola

E) move along some other curve

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

49. What magnitude impulse will give a 2.0-kg object a momentum change of magnitude +50 kg∙m/s?

A) + 25 N∙s

B) – 25 N∙s

C) + 50 N∙s

D) – 50 N∙s

E) + 100 N∙s

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

50. A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The average force on the club on the ball during the time T is:

A) mvT

B) mv/T

C) (1/2)mv²T

D) mv²/(2T)

E) mT²/(2v)

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

51. A 640-N acrobat falls 5.0 m from rest into a net. The net tosses him back up with the same speed he had just before he hit the net. The average upward force exerted on him by the net during this collision is:

A) 32 N

B) 64 N

C) 320 N

D) 640 N

E) impossible to determine from given data

Difficulty: E

Section: 9-4

Learning Objective 9.4.2

52. Sphere X, of mass 2 kg, is moving to the right at 10 m/s. Sphere Y, of mass 4 kg, is moving to the left at 10 m/s. The two spheres collide head-on. The magnitude of the impulse of X on Y is:

A) twice the magnitude of the impulse of Y on X

B) half the magnitude of the impulse of Y on X

C) one-fourth the magnitude of the impulse of Y on X

D) four times the magnitude of the impulse of Y on X

E) the same as the magnitude of the impulse of Y on X

Difficulty: E

Section: 9-4

Learning Objective 9.4.3

53. Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have:

A) greater speed than the other body

B) greater acceleration than the other body

C) smaller momentum than the other body

D) greater momentum than the other body

E) the same momentum as the other body

Difficulty: E

Section: 9-4

Learning Objective 9.4.3

54. A student's life was saved in an automobile accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag:

A) causes a much smaller change in momentum

B) exerts a much smaller impulse

C) causes a much smaller change in kinetic energy

D) exerts a much smaller force

E) does much more work

Difficulty: E

Section: 9-4

Learning Objective 9.4.3

55. A 25-kg box of books is dropped on the floor from a height of 1.1 m and comes to rest. What impulse did the floor exert on the box?

A) cannot be answered without knowing how long it took the box to stop

B) 22 kg∙m/s

C) 120 kg∙m/s

D) 270 kg∙m/s

E) 540 kg∙m/s

Difficulty: M

Section: 9-4

Learning Objective 9.4.4

56. The force on a particle is given by F(t) = 0.71 t + 1.2 t², in N. If the force acts from t = 0 to t = 2.0 s, the total impulse is:

A) 1.2 kg∙m/s

B) 1.9 kg∙m/s

C) 4.6 kg∙m/s

D) 4.8 kg∙m/s

E) 6.2 kg∙m/s

Difficulty: M

Section: 9-4

Learning Objective 9.4.5

57. The plot shows the force acting on an object as a function of time. Over the time the force is applied, the total impulse is:

A) 0 N∙s

B) 2 N∙s

C) 4 N∙s

D) 8 N∙s

E) cannot be determined without knowing the mass of the object

Difficulty: E

Section: 9-4

Learning Objective 9.4.6

58. A stream of gas consists of n molecules. Each molecule has mass m and speed v. The stream is reflected elastically from a rigid surface as shown. The magnitude of the change in the total momentum of the stream is:

A) 2mnv

B) 2mnv sin 30

C) mnv sin 30

D) mnv cos 30

E) mnv

Difficulty: E

Section: 9-4

Learning Objective 9.4.7

59. A 75-kg man is riding in a 30-kg cart at 2.0 m/s. He jumps off in such a way as to land on the ground with no horizontal velocity. The resulting change in speed of the cart is:

A) 0 m/s

B) 2.0 m/s

C) 3.0 m/s

D) 5.0 m/s

E) 7.0 m/s

Difficulty: E

Section: 9-5

Learning Objective 9.5.1

60. A shell is launched from a cannon and explodes mid-air. Which of the following is correct after the explosion?

A) Since the explosion exerts external forces on the shell, neither its horizontal momentum nor its vertical momentum is conserved.

B) Since the explosion exerts only internal forces on the shell, both its horizontal and vertical momenta are conserved.

C) Since the explosion exerts only internal forces on the shell, but gravity is an external force, neither its horizontal momentum nor its vertical momentum is conserved.

D) Since the explosion exerts only internal forces on the shell, but gravity is an external force, its horizontal momentum is conserved but its vertical momentum is not conserved.

E) Since the explosion exerts only internal forces on the shell, but gravity is an external force, its vertical momentum is conserved but its horizontal momentum is not conserved.

Difficulty: E

Section: 9-5

Learning Objective 9.5.2

61. An inelastic collision is one in which:

A) momentum is not conserved but kinetic energy is conserved

B) total mass is not conserved but momentum is conserved

C) neither kinetic energy nor momentum is conserved

D) momentum is conserved but kinetic energy is not conserved

E) the total impulse is equal to the change in kinetic energy

Difficulty: E

Section: 9-6

Learning Objective 9.6.1

62. A 4.0-N puck is traveling at 3.0 m/s. It strikes an 8.0-N puck, which is stationary. The two pucks stick together. Their common final speed is:

A) 1.0 m/s

B) 1.5 m/s

C) 2.0 m/s

D) 2.3 m/s

E) 3.0 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.1

63. An elastic collision is one in which:

A) momentum is not conserved but kinetic energy is conserved

B) total mass is not conserved but momentum is conserved

C) kinetic energy and momentum are both conserved

D) momentum is conserved but kinetic energy is not conserved

E) the total impulse is equal to the change in kinetic energy

Difficulty: E

Section: 9-6

Learning Objective 9.6.1

64. Whenever an object strikes a stationary object of equal mass:

A) the two objects cannot stick together

B) the collision must be elastic

C) the first object must stop

D) momentum is not necessarily conserved

E) none of the above

Difficulty: E

Section: 9-6

Learning Objective 9.6.0

65. In a one-dimensional collision,

A) a moving object strikes a stationary object, after which the objects move in arbitrary directions.

B) the objects must be moving along the same line before the collision, but may be moving in arbitrary directions after the collision.

C) one of the objects must remain at rest after the collision.

D) one of the objects must be at rest before the collision.

E) all motion, both before and after the collision, must be along the same line.

Difficulty: E

Section: 9-6

Learning Objective 9.6.2

66. A 64-kg woman stands on frictionless level ice with a 0.10-kg stone at her feet. She kicks the stone with her foot so that she acquires a velocity of 0.0017 m/s in the forward direction. The velocity acquired by the stone is:

A) 1.1 m/s forward

B) 1.1 m/s backward

C) 0.0017 m/s forward

D) 0.0017 m/s backward

E) none of these

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

67. A man is marooned at rest on level frictionless ice. In desperation, he hurls his shoe to the right at 15 m/s. If the man weighs 720 N and the shoe weighs 4.0 N, the man moves to the left at approximately:

A) 0 m/s

B) 2.1  10^–2 m/s

C) 8.3  10^–2 m/s

D) 15 m/s

E) 1.1 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

68. Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5 m/s. The final recoil speed of A is:

A) 0 m/s

B) 0.38 m/s

C) 0.43 m/s

D) 0.50 m/s

E) 1.0 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

69. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is:

A) –mv

B) –Mv/m

C) –mv/M

D) –v

E) mv/M

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

70. Bullets from two revolvers are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2. Gun #1 weighs three times as much as gun #2. The ratio of the momentum imparted to gun #1 to that imparted to gun #2 is:

A) 2:3

B) 3:2

C) 2:1

D) 3:1

E) 6:1

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

71. Cart A, with a mass of 0.2 kg, travels on a horizontal air track at 3 m/s and hits cart B, which has a mass of 0.4 kg and is initially at rest. After the collision the center of mass of the two cart system has a speed in m/s of:

A) 0 m/s

B) 1.0 m/s

C) 2.3 m/s

D) 2.5 m/s

E) 5.0 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

72. A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3 m/s as shown. After the sack rests on the flatcar, the speed of the flatcar is:

A) 0.6 m/s

B) 1.2 m/s

C) 1.8 m/s

D) 2.4 m/s

E) 3.6 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

73. A 3.00-g bullet traveling horizontally at 400 m/s hits a 3.00-kg wooden block, which is initially at rest on a smooth horizontal table. The bullet buries itself in the block without passing through. The speed of the block after the collision is:

A) 1.33 m/s

B) 0.40 m/s

C) 12.0 m/s

D) 12.6 m/s

E) 40.0 m/s

Difficulty: E

Section: 9-6

Learning Objective 9.6.3

74. A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the bullet was:

A) unknown since the heat generated in the collision was not given

B) 8.0  10² m/s

C) 24.0 m/s

D) 8.0 m/s

E) 2.4  10⁴ m/s

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

75. A 3.0-kg cart and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40 J. The speed of their center of mass is:

A) 0 m/s

B) 2.8 m/s

C) 4.0 m/s

D) 5.2 m/s

E) 8.0 m/s

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

76. Blocks A and B are moving toward each other. A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of –25 m/s. They suffer a completely inelastic collision. The kinetic energy lost during the collision is:

A) 0 J

B) 1250 J

C) 3750 J

D) 5000 J

E) 5600 J

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

77. For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as:

A) the total kinetic energy before the collision

B) the difference in the kinetic energies of the objects before the collision

C) 1/2Mv²_com, where M is the total mass and v_com is the velocity of the center of mass

D) the kinetic energy of the more massive body before the collision

E) the kinetic energy of the less massive body before the collision

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

78. A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of:

A) 0 N∙s

B) 4 N∙s

C) 6 N∙s

D) 9 N∙s

E) 12 N∙s

Difficulty: M

Section: 9-6

Learning Objective 9.6.3

79. Two identical carts travel at 1 m/s on a common surface. They collide head-on and are reported to rebound, each with a speed of 2 m/s. Then:

A) momentum was not conserved, therefore the report must be false

B) if some other form of energy were changed to kinetic during the collision, the report could be true

C) if the collision were elastic, the report could be true

D) if the surface were inclined, the report could be true

E) kinetic energy increased, therefore the report must be false

Difficulty: E

Section: 9-6

Learning Objective 9.6.0

80. A block moves at 5 m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks move along the x axis and the incident block has a speed of:

A) 1.8 m/s

B) 3.2 m/s

C) 5.0 m/s

D) 6.8 m/s

E) 7.1 m/s

Difficulty: H

Section: 9-6

Learning Objective 9.6.3

81. A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion:

A) is the same as the momentum of the projectile immediately before the explosion

B) has been changed into kinetic energy of the fragments

C) is less than the momentum of the projectile immediately before the explosion

D) is more than the momentum of the projectile immediately before the explosion

E) has been changed into radiant energy

Difficulty: E

Section: 9-6

Learning Objective 9.6.4

82. The law of conservation of momentum applies to a system of colliding objects only if:

A) there is no change in kinetic energy of the system

B) the coefficient of restitution is one

C) the coefficient of restitution is zero

D) the net external impulse is zero

E) the collisions are all elastic

Difficulty: E

Section: 9-6

Learning Objective 9.6.4

83. Two carts (A and B), having spring bumpers, collide as shown. Cart A has a mass of 2 kg and is initially moving to the right. Cart B has a mass of 3 kg and is initially stationary. When the separation between the carts is a minimum:

A) cart B is still at rest

B) cart A has come to rest

C) the carts have the same momentum

D) the carts have the same kinetic energy

E) the kinetic energy of the system is at a minimum

Difficulty: M

Section: 9-6

Learning Objective 9.6.0

84. Object A strikes the stationary object B head-on in an elastic collision. The mass of A is fixed, you may choose the mass of B appropriately. Then:

A) for B to have the greatest recoil speed, choose m_B = m_A

B) for B to have the greatest recoil momentum, choose m_B << m_A

C) for B to have the greatest recoil kinetic energy, choose m_B >> m_A

D) for B to have the least recoil speed, choose m_B = m_A

E) for B to have the greatest recoil kinetic energy, choose m_B = m_A

Difficulty: M

Section: 9-7

Learning Objective 9.7.1

85. Block A, with a mass of 2.0 kg, moves along the x axis with a velocity of 5.0 m/s in the positive x direction. It suffers an elastic collision with block B, initially at rest, and the blocks leave the collision along the x axis. If B is much more massive than A, the velocity of A after the collision is:

A) 0 m/s

B) +5.0 m/s

C) –5.0 m/s

D) +10 m/s

E) –10 m/s

Difficulty: E

Section: 9-7

Learning Objective 9.7.1

86. A very massive object traveling at 10 m/s strikes a light object, initially at rest, and the light object moves off in the direction of travel of the heavy object. If the collision is elastic, the speed of the lighter object is

A) 5.0 m/s

B) 10 m/s

C) 15 m/s

D) 20 m/s

E) Can't tell from the information given.

Difficulty: E

Section: 9-7

Learning Objective 9.7.1

87. Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (v_A, v_B) are:

A) 0, v/2

B) –v/3, 2v/3

C) –v, v

D) –2v/3, v/3

E) none of these

Difficulty: E

Section: 9-7

Learning Objective 9.7.1

88. Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of –25 m/s. They suffer an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is:

A) 0 J

B) 2500 J

C) 5000 J

D) 7500 J

E) 10000 J

Difficulty: M

Section: 9-7

Learning Objective 9.7.1

89. When a particle suffers a head-on elastic collision with another particle, initially at rest, the greatest fraction of kinetic energy is transferred if:

A) the incident particle is initially traveling very fast

B) the incident particle is traveling very slowly

C) the incident particle is much more massive than the target particle

D) the incident particle is much less massive than the target particle

E) the incident and target particle have the same mass

Difficulty: E

Section: 9-7

Learning Objective 9.7.1

90. Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:

A) 20 J

B) 8 J

C) 310 J

D) 125 J

E) 50 J

Difficulty: M

Section: 9-7

Learning Objective 9.7.1

91. If a projectile hits a stationary target, and the projectile stops while the target moves at the same speed as the incoming speed of the projectile,

A) the mass of the projectile is much less than the mass of the target.

B) the mass of the projectile is equal to the mass of the target.

C) the mass of the projectile is much greater than the mass of the target.

D) nothing can be said about the masses of the projectile and target without further information.

E) this is an unphysical situation and will not actually happen.

Difficulty: E

Section: 9-7

Learning Objective 9.7.2

92. If a projectile hits a stationary target, and the projectile rebounds and travels back the way it came,

A) the mass of the projectile is much less than the mass of the target.

B) the mass of the projectile is equal to the mass of the target.

C) the mass of the projectile is much greater than the mass of the target.

D) nothing can be said about the masses of the projectile and target without further information.

E) this is an unphysical situation and will not actually happen.

Difficulty: E

Section: 9-7

Learning Objective 9.7.2

93. If a projectile hits a stationary target, and the projectile continues to travel in the same direction,

A) the mass of the projectile is less than the mass of the target.

B) the mass of the projectile is equal to the mass of the target.

C) the mass of the projectile is greater than the mass of the target.

D) nothing can be said about the masses of the projectile and target without further information.

E) this is an unphysical situation and will not actually happen.

Difficulty: E

Section: 9-7

Learning Objective 9.7.2

94. A hockey puck of mass m traveling along the x axis at 4.5 m/s hits another identical hockey puck at rest. If after the collision the second puck travels at a speed of 3.5 m/s at an angle of 30° above the x axis, what is the final velocity of the first puck?

A) 1.0 m/s, 30° below the x axis

B) 2.3 m/s, 50° below the x axis

C) 2.8 m/s, 60° below the x axis

D) 3.0 m/s, 45° below the x axis

E) not enough information

Difficulty: M

Section: 9-8

Learning Objective 9.8.1

95. A hockey puck of mass m traveling along the x axis at 4.5 m/s hits another identical hockey puck at rest. If after the collision the second puck travels at a speed of 3.5 m/s at an angle of 30° above the x axis, is this an elastic collision?

A) Yes, since momentum is conserved.

B) No, since momentum is not conserved.

C) Yes, since kinetic energy is conserved.

D) No, since kinetic energy is not conserved.

E) Not enough information.

Difficulty: H

Section: 9-8

Learning Objective 9.8.2

96. The thrust of a rocket is

A) a gravitational force acting on the rocket

B) the force of the exiting fuel gases on the rocket

C) any force that is external to the rocket-fuel system

D) a force that arises from the reduction in mass of the rocket-fuel system

E) none of the above

Difficulty: E

Section: 9-9

Learning Objective 9.9.0

97. At one instant of time a rocket is traveling in outer space at 2500 m/s and is exhausting fuel at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500 m/s, relative to the rocket, the thrust is:

A) 0 N

B) 1.0  10⁵ N

C) 1.5  10⁵ N

D) 2.9  10⁵ N

E) 2.5  10⁵ N

Difficulty: E

Section: 9-9

Learning Objective 9.9.1

98. A rocket exhausts fuel with a velocity of 1500 m/s, relative to the rocket. It starts from rest in outer space with fuel comprising 80 per cent of the total mass. When all the fuel has been exhausted its speed is:

A) 3600 m/s

B) 2400 m/s

C) 1200 m/s

D) 880 m/s

E) 400 m/s

Difficulty: M

Section: 9-9

Learning Objective 9.9.2

99. A 1000-kg space probe is motionless in space. To start moving, its main engine is fired for 5 s during which time it ejects exhaust gases at 5000 m/s. At the end of this process it is moving at 20 m/s. The approximate mass of the ejected gas is:

A) 0.8 kg

B) 4 kg

C) 5 kg

D) 20 kg

E) 25 kg

Difficulty: M

Section: 9-9

Learning Objective 9.9.2

100. A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:

A) constant and in the forward direction

B) constant and in the backward direction

C) variable and in the forward direction

D) variable and in the backward direction

E) zero

Difficulty: E

Section: 9-9

Learning Objective 9.9.3