### Spring 2009 Physics 211 Hour Exam 2(25 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 111. The exam period was 90 minutes. THe mean score was 86.2; the median was 89. Click here to see the formula sheet that came with the exam.

### QUESTION 1**

The Work Kinetic-Energy Theorem is invalid if work is done by a non- conservative force.

(T)   True
(F)   False

### QUESTION 2**

This and the next question refer to the following situation:

A small block having a mass 0.1 kg starts at rest at the top of a frictionless track a height 1.7 m above the horizontal floor. It slides down the track and then around a loop-the-loop having a diameter of 0.6 m.

What is the normal force exerted by the track on the small block as it goes around the top of the loop?

(a)   6.2 N
(b)   5.6 N
(c)   4.9 N
(d)   3.8 N
(e)   2.4 N

### QUESTION 3*

After rounding the loop the block continues along the frictionless horizontal floor, running into the end of a horizontal spring whose other end is fixed. If the spring is compressed a distance of 0.05 m from its resting length as the block is (momentarily) brought to rest, what is the spring constant?

(a)   6.6 × 102 N/m
(b)   8.6 × 102 N/m
(c)   1.3 × 103 N/m
(d)   1.8 × 103 N/m
(e)   2.7 × 103 N/m

### QUESTION 4*

A block of mass M is initially at rest on a horizontal, frictionless table. A bullet of mass m is fired from the left with an initial horizontal speed v0 toward the block, as shown in the upper diagram. (Ignore the effect of the gravitational force on the bullet.) The bullet hits the block and becomes lodged inside it.

After the block and bullet start moving to the right, a second bullet of mass m is now fired horizontally from the right with an initial speed v0 toward the block. The second bullet hits the block and becomes lodged inside it.

Which one of the following describes the motion of the block after both bullets are lodged inside it?

(a)   The final velocity is to the left.
(b)   The final velocity is zero.
(c)   The final velocity is to the right.

### QUESTION 5**

A pendulum is released from rest, as shown in Figure A. When the bob is directly below the pivot point, the ideal string encounters an ideal peg, about which it begins to wrap, as shown in Figures B and C. The peg is higher than the initial height of the pendulum.

In Figure C, the bob rises up to a height

(a)   equal to the original height of the bob in Figure A.
(b)   greater than the original height of the bob in Figure A.
(c)   less than the original height of the bob in Figure A.

### QUESTION 6*

This and the next question refer to the following situation:

A planet of mass M and radius R and a smaller planet of radius R/2 and mass M/8 are separated by a distance 6R between their centers. How far from the center of the larger planet is the center of mass of this two-body system?

(a)   2 R / 3
(b)   4 R / 9
(c)   R / 2
(d)   3 R / 5
(e)   3 R / 8

### QUESTION 7*

The larger planet explodes into two fragments, as shown. The center-of-mass of the three-body system is now
(a)   closer to the smaller planet.
(b)   further from the smaller planet.
(c)   the same distance from the smaller planet.

### QUESTION 8*

A stationary soccer ball, mass 0.43 kg, undergoes the impulse shown in the figure. What is the final speed of the soccer ball after the impulse is complete?

(a)   2.71 m/s
(b)   4.13 m/s
(c)   6.33 m/s
(d)   8.37 m/s
(e)   10.43 m/s

### QUESTION 9*

A putty ball of mass M = 0.5 kg is traveling horizontally at v = 2 m/s. (Ignore the effects of gravity). It strikes a block of the same mass, which is adjacent to a relaxed ideal spring attached to an infinitely massive wall with a spring constant of k = 4 N/m. The putty ball sticks to the block. After the collision, the spring is compressed. What is the maximum compression of the spring?

(a)   0.1 m
(b)   0.2 m
(c)   0.3 m
(d)   0.4 m
(e)   0.5 m

### QUESTION 10**

A potential energy function can only be defined for conservative forces.

(T)   True
(F)   False

### QUESTION 11***

This and the next question refer to the following situation:

A block of mass m1 = 12.5 kg hangs from the ceiling on an ideal, massless spring with spring constant k = 65 N/m. With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m2 = 10 kg is tied to the first with a massless string, the spring stretches an additional h0 = 1.5 m.

The string is cut so that mass m2 falls away. What is the maximum velocity of mass m1?

(a)   2.77 m/s
(b)   3.42 m/s
(c)   4.68 m/s
(d)   5.21 m/s
(e)   6.39 m/s

### QUESTION 12**

When the mass is at its highest point, the distance between the ceiling and the mass is D (labeled in the figure on the right). Which one of the following is true?

(a)   D  <  L - h0
(b)   D  =  L - h0
(c)   D  >  L - h0

### QUESTION 13*

This and the next question refer to the following situation:

Two discs are free to move without friction on a horizontal table. The 0.4 kg disc is initially at the position (x = 0, y = 1.0) m, moving with velocity (vx = 3.0, vy = 0) m/s. The 0.6-kg disc is initially at (x = 1.5, y = 0) m, moving with velocity (vx = 0, vy = 2.0) m/s.

The figure displays the initial conditions for the two discs in the x-, y-coordinates.

The initial velocity of the center of mass of the two-disc system is:

(a)   (vx, vy) = (3.0, 2.0) m/s
(b)   (vx, vy) = (2.0, 3.0) m/s
(c)   (vx, vy) = (2.7, 2.0) m/s
(d)   (vx, vy) = (1.8, 1.8) m/s
(e)   (vx, vy) = (1.2, 1.2) m/s

### QUESTION 14*

The two blocks collide at some point in the x-y plane. What is the velocity of the center of mass after the collision?

(a)   less than before the collision
(b)   the same as before the collision
(c)   It depends on whether the collision is elastic or inelastic.

### QUESTION 15*

The centers of three spheres having masses 1 kg, 2 kg, and 3 kg are placed at the corners of an equilateral triangle whose sides are each 1 meter long, as shown below. How far from the center of the 1 kg sphere is the center of mass of the system?

(a)   0.33 m
(b)   0.50 m
(c)   0.67 m
(d)   0.73 m
(e)   1.00 m

### QUESTION 16*

This question and the next two refer to the following situation:

A box with mass M = 10 kg is pulled across a floor by a rope. There is friction between the box and the floor. The tension in the rope is T = 25 N. Consider an interval during which the box moves a distance of Δx = 3 m and its velocity increases from 2 m/s to 3 m/s.

How much work (WT) is done on the box by the rope?

(a)   0 J
(b)   45 J
(c)   65 J
(d)   75 J
(e)   125 J

### QUESTION 17*

How much work (Wnet) is done on the box by the net force ?

(a)   0 J
(b)   15 J
(c)   25 J
(d)   65 J
(e)   125 J

### QUESTION 18**

Which one of the following is a valid expression for the coefficient of kinetic friction between the box and the floor?

(a)   WT / (Mg Δx)
(b)   Wnet / (Mg Δx)
(c)   Mg Δx / WT
(d)   (WT - Wnet) / (Mg Δx)
(e)   (Wnet - WT) / (Mg Δx)

### QUESTION 19*

This and the next question refer to the following situation:

A man is standing at one end of a plank of length L = 10 m. The man has mass Mman = 100 kg and the plank has mass Mplank = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass Mrock = 200 kg. The center of mass of the man+plank+rock is 6.5 m from the end of the plank where the man is standing.

The man walks to the other end of the plank and sits down on the rock. How far did the plank move along the ice?

(a)   0 m
(b)   1.3 m
(c)   1.7 m
(d)   2.9 m
(e)   3.3 m

### QUESTION 20*

As the man walks along the plank, the momentum of the plank+man+rock is not conserved because the man is exerting a force on the plank.

(T)   True
(F)   False

### QUESTION 21*

This question and the next two refer to the following situation:

A glider of mass m1 = 0.4 kg slides on a frictionless track with initial velocity v1,i = 1.8 m/s. It hits a stationary glider of mass m2 = 0.8 kg. A spring attached to the first glider makes the collision elastic. What are the final velocities of the gliders?

(a)   v1,f = -0.6 m/s, v2,f = 1.2 m/s
(b)   v1,f = -0.2 m/s, v2,f = 0.8 m/s
(c)   v1,f = -1.4 m/s, v2,f = 2.2 m/s
(d)   v1,f = -0.4 m/s, v2,f = 0.4 m/s
(e)   v1,f = -1.4 m/s, v2,f = 1.0 m/s

### QUESTION 22*

If the mass of the stationary glider were increased, but everything else was unchanged, the final speed of the other glider would

(a)   increase.
(b)   decrease.
(c)   stay the same.

### QUESTION 23*

Imagine that the spring is removed. Now when the gliders collide, they stick together. Which one of the following statements is correct?

(a)   Kinetic energy and momentum are conserved in the collision.
(b)   Kinetic energy is conserved, but momentum is not conserved in the collision.
(c)   Momentum is conserved, but kinetic energy is not conserved in the collision.

### QUESTION 24**

This and the next question refer to the following situation:

Two identical disks of mass M are sitting atop a frictionless table. For disk number 1, a string is attached to the center of mass of the disk. For disk number 2, the string is wrapped around the disk. Each string is pulled on by a force F which has the same direction and magnitude for both disks. The center of mass of disk 1 has acceleration A1 and the center of mass of disk 2 has acceleration A2 as shown in the figure.

How do A1 and A2 compare?

(a)   A1 > A2
(b)   A1 = A2
(c)   A1 < A2

### QUESTION 25*

In a slightly different configuration, the two disks have different masses, with M3 > M4. Here both strings are connected to the centers of mass of the two disks, as shown in the figure. Initially, both disks are at rest. Each string is pulled on by a force F which has the same direction and magnitude for both disks. At some later moment, the disks have momentum P3 and P4 as shown in the figure.

(a)   P3 > P4
(b)   P3 = P4
(c)   P3 < P4

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.