Question 1

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:

Accepted Answer

A)  3600 m/s 
B)  2400 m/s 
C)  1200 m/s 
D)  880 m/s 
E)  400 m/s

Question 2

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

Accepted Answer

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

Question 3

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 4

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:

Accepted Answer

A)  2mnv 
B)  2mnv sin 30  $\degree$ 
C)  mnv sin 30  $\degree$ 
D)  mnv cos 30  $\degree$ 
E)  mnv

Question 5

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:

Accepted Answer

A)  20 J 
B)  8 J 
C)  310 J 
D)  125 J 
E)  50 J

Question 6

Force:

Accepted Answer

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

Question 7

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 8

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

Accepted Answer

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.

Question 9

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 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.

Accepted Answer

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

Question 11

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 12

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:

Accepted Answer

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

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

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 15

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:

Accepted Answer

A)  0.25 g 
B)  0.50 g 
C)  0.67 g 
D)  0.75 g 
E)  1.0 g

Question 16

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 17

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 18

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 19

Which one of the following statements is true?

Accepted Answer

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

Question 20

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

Exam 9: Center of Mass and Linear Momentum