Question 1

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 (vA, vB)are:

Accepted Answer

A) 0, v/2 
B) -v/3, 2v/3 
C) -v, v 
D) -2v/3, v/3 
E) none of these

Question 2

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?

Accepted Answer

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.

Question 3

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:

Accepted Answer

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

Question 4

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?

Accepted Answer

A) 4 m 
B) 5 m 
C) 6 m 
D) 10 m 
E) need to know the forces they exert

Question 5

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:

Accepted Answer

A) 3.0 N∙s 
B) 6.0 N∙s 
C) 9.0 N∙s 
D) 15 N∙s 
E) 29 N∙s

Question 6

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?

Accepted Answer

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

Question 7

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:

Accepted Answer

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

Question 8

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:

Accepted Answer

A) 0 J 
B) 0.31 J 
C) 0.61 J 
D) 0.81 J 
E) 1.2 J

Question 9

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

Accepted Answer

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.

Question 10

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?

Accepted Answer

A) 8.0 m/s 
B) 14 m/s 
C) 20 m/s 
D) 27 m/s 
E) 34 m/s

Question 11

If the total momentum of a system is changing:

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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:

Accepted Answer

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

Question 14

Whenever an object strikes a stationary object of equal mass:

Accepted Answer

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

Question 15

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:

Accepted Answer

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

Question 16

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?

Accepted Answer

A) 8.0 m/s 
B) 21 m/s 
C) 49 m/s 
D) 64 m/s 
E) 65 m/s

Question 17

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:

Accepted Answer

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

Question 18

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:

Accepted Answer

A) 1.0 m 
B) 3.3 m 
C) 10 m 
D) 12 m 
E) 17 m

Question 19

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:

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 20

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:

Accepted Answer

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

Exam 9: Center of Mass and Linear Momentum

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:

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:

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 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 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?

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

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?

If the total momentum of a system is changing:

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

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:

Whenever an object strikes a stationary object of equal mass:

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:

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 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 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 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 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:

Exam 9: Center of Mass and Linear Momentum

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 (vA, vB) are:

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:

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 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 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?

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

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?

If the total momentum of a system is changing:

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

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:

Whenever an object strikes a stationary object of equal mass:

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:

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 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 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 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 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:

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:

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?

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?