### Spring 2010 Physics 101 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 114. The exam period was 90 minutes. The mean score was 67.8; the median was 68. Click here to see page1 page2 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s2 downward and ignore any effects due to air resistance.

### QUESTION 1*

This question and the next one concern the same situation:

A solid, uniform cube 1 meter on a side is pushed against a narrow step on the floor (see figure); the block is then free to rotate about the axis marked with a solid black dot. A force F = 13 N is applied horizontally to the edge opposite the narrow step. What is the magnitude of the torque around the axis marked by the black dot due to the force F ?

(a)   7 N⋅m
(b)   9 N⋅m
(c)   11 N⋅m
(d)   13 N⋅m
(e)   15 N⋅m

### QUESTION 2***

Suppose the mass of the cube is 15 kg. What is the minimum torque required to tip the block up and cause it to rotate around the axis?

(a)   8 N⋅m
(b)   15 N⋅m
(c)   32 N⋅m
(d)   64 N⋅m
(e)   74 N⋅m

### QUESTION 3***

This question and the next one concern the same situation:

Consider a ladder of length 5 m leaning against a house at an angle of 25° from the vertical. The mass of the ladder is 10 kg and the interaction between the wall and the ladder is frictionless. Assume the mass of the ladder is distributed uniformly. What is the normal force from the wall on the ladder?

(a)   22.8 N
(b)   61.4 N
(c)   77.5 N
(d)   88.2 N
(e)   98.3 N

### QUESTION 4*

A person stands on the ladder and walks up. Does the magnitude of the normal force from the wall increase or decrease?

(a)   increases
(b)   decreases

### QUESTION 5*

The recent earthquake in Chile shortened the length of the day by 1.26 millionths of a second. Assume no external torques acting on the earth. Did the rotational energy of the earth increase or decrease?

(a)   increased
(b)   decreased

### QUESTION 6***

A ball (solid uniform sphere) rolls up a plane that is inclined at an angle of 30° to the horizontal, without slipping. Would the angular acceleration be the same if the ball were rolling down the hill?

(a)   yes
(b)   no

### QUESTION 7*

This question and the next one concern the same situation:

A uniform solid disk of mass 3.2 kg and radius 0.25 m is spinning with an angular frequency of 40 rad/s around the axis at the center of mass, perpendicular to the disk. What is the magnitude of the disk's angular momentum?

(a)   1 kg m2/s
(b)   2 kg m2/s
(c)   4 kg m2/s
(d)   8 kg m2/s
(e)   16 kg m2/s

### QUESTION 8***

Suppose a frictional force of 2 N is applied at the rim of the disk. What is the magnitude of the angular acceleration of the disk?

### QUESTION 9*

This question and the next two concern the same situation:

A ball falls vertically from the initial height of 2.1 m with no initial velocity to the floor and bounces vertically, reaching the highest point 1.7 m from the floor as illustrated. Take the origin of the potential energy of the ball to be that on the floor. The mass of the ball is 0.120 kg.

What is the loss of mechanical energy due to bouncing?

(a)   13% of the initial potential energy
(b)   19% of the initial potential energy
(c)   24% of the initial potential energy
(d)   28% of the initial potential energy
(e)   31% of the initial potential energy

### QUESTION 10**

What is the magnitude of the impulse on the ball from the floor when the ball bounces?

(a)   0.27 N⋅s
(b)   0.39 N⋅s
(c)   0.84 N⋅s
(d)   1.15 N⋅s
(e)   1.46 N⋅s

### QUESTION 11**

Suppose instead that the mechanical energy is conserved during the bounce. Then the magnitude of the impulse on the ball from the floor would be

(a)   larger than the case with energy loss.
(b)   smaller than the case with energy loss.
(c)   Insufficient information is provided to give a definite answer.

### QUESTION 12**

A mass moving at a constant velocity in the x direction splits into two pieces without any external influence. After the split, the two pieces have velocity V1 and V2, respectively. They have the same x-components (see the illustration; only their x-components are accurately given).

In this event

(a)   both energy and momentum are conserved.
(b)   energy is conserved, but not momentum.
(c)   momentum is conserved, but not energy.

### QUESTION 13**

There are two identical blocks (with the same mass) in a frictionless straight horizontal trough. Block B is initially stationary, and block A runs into block B. Can A reverse its direction of motion after collision?

(a)   No, never.
(b)   Yes,
(c)   It depends on the details of the collision.

### QUESTION 14**

This question and the next one concern the same situation:

Two dry ice pucks slide on a horizontal, frictionless surface. Puck A, which is 2 kg, moves at speed 7 m/s in the positive x direction and Puck B, which is 1 kg, moves at speed 8 m/s in the negative y direction as shown in the figure. The pucks collide near the star in the figure. After the collision Puck B is moving in the positive x direction, while Puck A is moving in the direction that makes 45° with the positive x-axis as illustrated.

Find the speed of Puck A after the collision.

(a)   1 m/s
(b)   2 m/s
(c)   2√2 m/s
(d)   4 m/s
(e)   4√2 m/s

### QUESTION 15***

What was the magnitude of the impulse on Puck B due to Puck A when they collided?

(a)   2 N⋅s
(b)   4 N⋅s
(c)   6 N⋅s
(d)   8 N⋅s
(e)   10 N⋅s

### QUESTION 16**

This question and the next one concern the same situation:

There is a slope with height h and the length of the slope L = 20 m as illustrated in the figure. A solid uniform cylinder of radium R = 0.2 m is at the top of the slope starting from rest. It rolls down the slope without any slip.

When the disk reaches the end of the slope, its center of mass has a speed of 4 m/s. What is the height h of the slope?

(a)   0.73 m
(b)   0.92 m
(c)   1.22 m
(d)   1.4 m
(e)   1.9 m

### QUESTION 17***

What is the torque on the disk around its center of mass due to the frictional force when it is rolling down the slope? You may assume that the moment of inertia of the disk is 0.03 kg⋅m2.

(a)   0.03 N⋅m
(b)   0.06 N⋅m
(c)   0.09 N⋅m
(d)   0.12 N⋅m
(e)   0.15 N⋅m

### QUESTION 18**

Consider two ways, A and B, for a ball to move from a height z = h to the ground at z = 0:
A) dropping in free fall

B) rolling without slipping down a plane that has an angle α with the horizontal plane (the ground)

Which one of the following is true instantaneously before the ball hits the ground?

(a)   The kinetic energy of case A is greater than case B.
(b)   The kinetic energy of case B is greater than case A.
(c)   The kinetic energy in both cases is the same.

### QUESTION 19*

Two students, George and Steve, run up a flight of stairs. Each student expends the same power to complete this task. George runs up in 5 seconds, and Steve runs up in 3 seconds. George weighs 200 pounds. How much does Steve weigh?

(a)   120 pounds
(b)   200 pounds
(c)   240 pounds
(d)   300 pounds
(e)   333 pounds

### QUESTION 20**

A mass (the solid ball in the figure) is circulated at a constant speed completely around two different paths (see figure). The area enclosed in path A is 4 times the area enclosed by path B. Gravity acts vertically.

(a)   More work is done by gravity in path A than in path B.
(b)   More work is done by gravity in path B than on path A.
(c)   The work done by gravity in both cases is identical.

### QUESTION 21**

Two brass balls with the same diameter roll down an inclined plane. They both start rolling down the ramp at the same time from the same place at the top of the ramp. Ball A is solid brass, and ball B is a hollow brass ball with a shell thickness only 1/16th of the radius. Both balls start from rest. Which ball arrives at the bottom first?

(a)   ball A
(b)   ball B
(c)   They both arrive at the bottom at the same time.

### QUESTION 22**

A pendulum consists of a point mass of 5 kg and is hanging from a massless string of 2 meters. You pull the point mass to a height 1 meter from the resting position, and then let the ball go. What is the angular velocity of the pendulum when the point mass is exactly at the lowest point?.

### QUESTION 23**

Consider two solid brass cylinders; cylinder A has a radius of 10 cm, and cylinder B has a radius of 20 cm. The cylinders have the same length. Both cylinders are released from the top of an inclined plane. When the cylinders reach the bottom of the plane, which cylinder has the greatest rotational kinetic energy?

(a)   cylinder A
(b)   cylinder B
(c)   Both have the same rotational kinetic energy.

### QUESTION 24**

Consider two pendulums with identical balls hanging from massless strings. The length of the smaller pendulum is ½ that of the larger pendulum and both balls at the minimum have the same distance to the ground. If both balls are raised to the same height h (compared to their minimum height - that is, the bottom), which one of the following statements is true?

(a)   The angular velocity of the smaller pendulum is greater than the angular velocity of the larger pendulum at the minimum position of the swinging pendulum.

(b)   The translational velocity of the larger pendulum is larger than the translational velocity of the smaller pendulum ball at the minimum position of the swinging pendulum.

(c)   The angular velocities of both pendulums are identical at the minimum position of the swinging pendulum.

### QUESTION 25**

A freely hanging block of mass 5 kg is attached to a massless string, which is wrapped several times around a pulley (solid cylinder) of mass 10 kg and radius 0.1 m (see diagram). There is no friction in the pulley mechanism. What is the acceleration of the block?

(a)   2.9 m/s2
(b)   3.9 m/s2
(c)   4.9 m/s2
(d)   5.9 m/s2
(e)   6.9 m/s2

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.