### Spring 2006 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 113. The exam period was 90 minutes. The mean score was75.2; the median was 75. 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 and the next three questions concern the same situation:

A solid spherical ball with mass M = 7 kg, radius R = 0.3 m, and initial velocity vi = 5 m/s rolls without slipping up a ramp and reaches the top. (Recall I = 2/5 M R2 for a solid uniform sphere.)

Calculate Li, the initial angular momentum of the ball around its rotation axis before it goes up the ramp.

(a)   Li = 3.57 kg m2/s
(b)   Li = 4.20 kg m2/s
(c)   Li = 8.62 kg m2/s
(d)   Li = 13.3 kg m2/s
(e)   Li = 35 kg m2/s

### QUESTION 2**

Compare Li the initial angular momentum of the ball around its rotation axis, with Lf the final angular momentum of the ball around its rotation axis after it goes up the ramp.

(a)   Li < Lf
(b)   Li = Lf
(c)   Li > Lf

### QUESTION 3*

Calculate E, the total kinetic energy of the ball before it goes up the ramp.

(a)   E = 67.5 J
(b)   E = 84.3 J
(c)   E = 98.1 J
(d)   E = 123 J
(e)   E = 152 J

### QUESTION 4**

Calculate vf the final velocity of the ball after it has gone up the ramp.

(a)   vf = 1.49 m/s
(b)   vf = 3.15 m/s
(c)   vf = 3.82 m/s
(d)   vf = 4.10 m/s
(e)   vf = 5.00 m/s

### QUESTION 5**

This and the next question concern the same situation:

You have your bicycle upside down for repair. The front wheel is free to rotate about its axis and is perfectly balanced except for the 0.025 kg valve stem 0.3 m from the rotation axis. The location of the stem is at an angle θ with respect to the horizontal, as shown in the figure. Gravity points downward in the figure.

For which of the following values of θ is the torque about the wheel’s axis due to the weight of the stem the smallest?

(a)   0°
(b)   45°
(c)   90°

### QUESTION 6**

If θ = 24°, what is the resulting torque about the wheel's axis?

(a)   0.176 Nm
(b)   0.363 Nm
(c)   0.014 Nm
(d)   0.067 Nm
(e)   0.214 Nm

### QUESTION 7**

This and the next question concern the same situation:

A uniform board of length L and weight W is supported in two places: one on the extreme left end and the other 2L/3 from the left end. What is the force exerted by the right support on the board?

(a)   3W/4
(b)   W/2
(c)   2W/3
(d)   W
(e)   3W/2

### QUESTION 8**

Now a box is placed on the extreme right end of the board. (Assume that the center of mass of the box sits at the very end of the board.) What is the maximum weight of the box such that the board does not tip?

(a)   W/4
(b)   W/2
(c)   W
(d)   2W
(e)   4W

### QUESTION 9**

Consider a thin rectangular board whose length L is larger than its width W, as shown in the figure. Three forces, A, B, and C of identical magnitude are applied at the corner in the plane of the board.

Which force results in the largest torque about an axis perpendicular to the plane of plane of the board and passing through its center?

(a)
(b)
(c)

### QUESTION 10*

This picture shows two different dumbbell shaped objects. Object A has two balls of mass m separated by a distance 2L, and object B has two balls of mass 2m separated by a distance L. Which of the objects has the largest moment of inertia for rotations around the x-axis? (Assume the balls can be treated as point masses and the rods are massless).

(a)   object A
(b)   object B
(c)   Both objects have the same moment of inertia about the x axis.

### QUESTION 11**

This and the next question concern the same situation:

A star is a uniform sphere of mass M and radius R. It rotates about its center with angular velocity ω. The star then collapses to radius R/10 (with the mass still M). What is the angular velocity of the star after its collapse? Note that there are no external torque on the star during the collapse.

(a)   ω / 100
(b)   ω / 10
(c)   ω
(d)   10 ω
(e)   100 ω

### QUESTION 12**

How is the kinetic energy of the star changed as a result of its collapse?

(a)   It increases.
(b)   It decreases.
(c)   It stays the same.

### QUESTION 13*

This and the next question concern the same situation:

A 0.125 kg ball is dropped from a height h above the ground and is observed to be traveling downward with a speed of 7 m/s just before hitting the ground. It bounces back up to a height of 2 meters. Neglect any energy losses due to the friction with the air.

From what height h was the ball dropped?

(a)   h = 1.5 m
(b)   h = 2.1 m
(c)   h = 2.5 m

### QUESTION 14***

The ball is in contact with the floor for 0.07 seconds. What is the average force F exerted on the ball by the floor?

(a)   F = 13 N
(b)   F = 18 N
(c)   F = 24 N
(d)   F = 28 N
(e)   F = 37 N

### QUESTION 15**

This and the next question concern the same situation:

An 85 kg bobsled starts from rest at the top of a frictionless course with a net 80 meter vertical drop. The bobsledder starts by running and pushing the sled with a constant force F over the first 15 meter flat section. The bobsled is observed to be traveling 45 m/s when it reaches the bottom of the run (before applying the brakes to stop).

What is the minimum average force F the bobsledders must have applied over those 15 meters to accelerate the bobsled at the start of the run?

(a)   1300 N
(b)   1800 N
(c)   4300 N

### QUESTION 16**

What is the minimum distance required to stop the sled at the bottom of the hill, if the coefficient of kinetic friction between the sled and the snow is 0.89 when the brake is being applied?

(a)   71 m
(b)   90 m
(c)   116 m
(d)   138 m
(e)   156 m

### QUESTION 17*

This and the next question concern the same situation:

Two blocks are sliding to the right on a frictionless surface and collide as shown below. Before the collision, the block M on the left has a speed of 4 m/s, and block 3M has a speed of 1 m/s. After the collision the right block (3M) is observed to travel to the right with speed 3 m/s.

What is the velocity of the 1M-block after the collision?

(a)   2 m/s to the left
(b)   5 m/s to the left
(c)   0 m/s
(d)   2 m/s to the right
(e)   5 m/s to the right

### QUESTION 18**

The total kinetic energy of the two blocks was conserved in this collision.

(T)   True
(F)   False

### QUESTION 19*

This and the following three questions concern the same situation:

A 75 kg student (represented by the solid black circle) standing at R=0.8 m from the center of a merry-go-round that is rotating with angular velocity ω = 2.5 radians/second. The merry-go-round alone has a moment of inertia of 599 kg-m2

What is the speed of the student as he goes around standing on the rim of the merry-go-round?

(a)   2.0 m/s
(b)   3.5 m/s
(c)   4.3 m/s

### QUESTION 20**

What is the minimum coefficient of static friction between the student and the merry-go-round, so that he does not slide off?

(a)   0.36
(b)   0.51
(c)   0.69
(d)   0.72
(e)   0.93

### QUESTION 21*

After rotating at the angular speed of 2.5 radians/second, the merry-go-round slows down with a constant angular acceleration stopping after 4 complete revolutions. What is the magnitude of the angular acceleration of the merry-go-round?

### QUESTION 22**

Assume again that the 75 kg student is standing at R=0.8 on the disk and that the disk rotates with a constant angular velocity.

An external torque t is applied to the disk and the student standing on it. The torque slows down the rotation a constant angular acceleration of α = -65 rad/s2. What is the magnitude of the applied torque? That is, what is the absolute value of the average torque on the merry-go-round while it is slowing down?

(a)   τ = 21 N-m
(b)   τ = 119 N-m
(c)   τ = 3710 N-m
(d)   τ = 40070 N-m
(e)   τ = 42060 N-m

### QUESTION 23**

A 1.5 kg block slides down a ramp that has a slope of 25° as shown below. The block starts from rest, and is observed to be traveling 3 m/s after it has slid 2.3 meters down the ramp. Calculate the work done by friction as the block slid 2.3 meters down the ramp.

(a)   Wf = -34 J
(b)   Wf = -15 J
(c)   Wf = -7.5 J
(d)   Wf = -0.8 J
(e)   Wf = 0 J

### QUESTION 24**

This and the next question concern the same situation:

Two disks are traveling on a frictionless surface and collide. Before the collision, the 1M disk is traveling 3 m/s in the positive x direction, and the 2M disk is traveling 2 m/s in the positive y direction as shown below. The two disks collide and stick together. (Gravity is perpendicular to the plane of the frictionless surface, i.e. perpendicular to the x-y plane)

Calculate the x component of the velocity of the two disks after the collision.

(a)   vx = 1 m/s
(b)   vx = 2 m/s
(c)   vx = 3 m/s

### QUESTION 25*

Calculate the y component of the velocity after the collision.

(a)   vy = 1 m/s
(b)   vy = 1.3 m/s
(c)   vy = 2 m/s

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.