### Fall 1999 Physics 101 Hour Exam 3(26 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 ***.

This exam consists of 26 questions; 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 119. When the exam was given, the minimum "A" score was 106; the minimum "B" was 92; the minimum "C" was 77; the minimum "D" was 59. The mean was 97.8; the median was 101. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

This and the next four questions are about the following 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. (Recall I = 2/5 M R2 for a solid 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 = 3.81 m/s
(d)   vf = 4.10 m/s
(e)   vf = 5.00 m/s

### QUESTION 5**

Next a hoop (I = MR2), with the same mass, radius, and initial velocity vi as the ball is rolled up the ramp. How does vhoop, the velocity of the hoop at the top of the ramp compare with vball the velocity of the ball at the top of the ramp?

(a)   vhoop < vball
(b)   vhoop = vball
(c)   vhoop > vball

### QUESTION 6*

This and the next three questions are about the following situation:

Mats is standing on a turntable in class holding a weight in each hand a distance 0.75 meters from the center of his body. He is originally rotating with an angular frequency w = 0.3 rad/s. He pulls the weights in so they are only 0.25 meters from the axis of rotation. The original moment of inertia of Mats, the turntable and the weights is Io = 8 kg m2. The final moment of inertia of Mats, the turntable and the weights is If = 5 kg m2. (For these four questions, assume that friction doesn't dissipate any energy.)

Calculate the original moment of inertia I for the two weights held a distance of d = 0.75 meters from Mats. (Treat the weights as point particles).

(a)   I = 2.90 kg m2
(b)   I = 3.38 kg m2
(c)   I = 4.82 kg m2
(d)   I = 5.26 kg m2
(e)   I = 6.00 kg m2

### QUESTION 7*

What is Mats' final angular velocity wf?

### QUESTION 8*

As Mats pulls the weights in, the total rotational kinetic energy of Mats, the turntable and the weights

(a)   increases.
(b)   remains the same.
(c)   decreases.

### QUESTION 9*

As Mats pulls the weights in, the total angular momentum of Mats, the turntable, and the weights

(a)   increases.
(b)   remains the same.
(c)   decreases.

### QUESTION 10*

This and the next four questions are about the following situation:

A block of mass 3.0 kg resting on a horizontal frictionless surface is attached to a spring with force constant k = 200 N/m. A force of 300 N is applied to the block in the x-direction, thereby compressing the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate.

What is the maximum compression of the spring?

(a)   0.4 m
(b)   0.9 m
(c)   1.2 m
(d)   1.5 m
(e)   1.9 m

### QUESTION 11*

How many cycles does the block undergo in a time of 10 seconds?

(a)   13
(b)   52
(c)   67
(d)   95
(e)   110

### QUESTION 12**

Which function best describes the position of the block as a function of time where x = 0 corresponds to the relaxed spring?

(a)   x(t) = A sin(wt)
(b)   x(t) = A cos(wt)

### QUESTION 13*

Which one of these plots best represents the kinetic energy of the block as a function of time?

(a)
(b)
(c)

### QUESTION 14*

Which one of the above plots best represents the sum of the potential and kinetic energy of the mass and spring as a function of time?

(a)
(b)
(c)

### QUESTION 15*

This and the next two questions are about the following situation:

These three questions are concerned with similar physical situations. In each situation you have an oscillator with a period of 1 second on Earth. You plan to bring the oscillator to planet X, where the force of gravity is two times that on earth (gX = 19.6 m/s2). You want to modify the oscillator so that it will have period of 1 second on planet X. In each of the following problems below, select the modification that will best achieve this.

Your oscillator is a simple pendulum consisting of a small sphere of mass M hanging vertically from a massless string of length L.

(a)   Reduce the mass to M/2.
(b)   Reduce the length to L/2.
(c)   Increase the length to 2 L.
(d)   Increase the length to 4 L.
(e)   Do nothing.

### QUESTION 16*

Your oscillator is a block of mass M attached to a horizontal spring of force constant k.

(a)   Reduce the mass to M/2.
(b)   Reduce the spring constant to k/2.
(c)   Increase the spring constant to 2k.
(d)   Increase the spring constant to 4k.
(e)   Do nothing.

### QUESTION 17**

Your oscillator is a block of mass M attached to a vertical spring of force constant k.

(a)   Reduce the spring constant.
(b)   Increase the spring constant.
(c)   Do nothing.

### QUESTION 18*

This and the next three questions are about the following situation:

Hose A has an inner radius of 2.4 cm, and water flows through it with a speed of 5 m/s. Using this hose, how much time t does it take to fill a pool that has a volume of 75 m3?

(a)   t = 8.3 x 103 s
(b)   t = 6.2 x 103 s
(c)   t = 3.9 x 103 s
(d)   t = 4.4 x 104 s
(e)   t = 5.8 x 104 s

### QUESTION 19*

Suppose the output end of hose A is attached to hose B, which has a smaller inner radius. If the speed of the water in hose A is unchanged, and the speed of the water in hose B is measured to be 45 m/s, what is rB the radius of hose B?

(a)   rB = 0.4 cm
(b)   rB = 0.8 cm
(c)   rB = 0.6 cm
(d)   rB = 1.2 cm
(e)   rB = 1.6 cm

### QUESTION 20*

If PA is the pressure in hose A, and PB is the pressure in hose B, calculate the difference in pressures PA-PB. Be careful with the sign and assume the hoses are both horizontal.

(a)   PA - PB = -1.5 x 106 Pa
(b)   PA - PB = -1.0 x 106 Pa
(c)   PA - PB = 0 Pa
(d)   PA - PB = +1.0 x 106 Pa
(e)   PA - PB = +1.5 x 106 Pa

### QUESTION 21**

Now suppose the hoses are turned around so that water is running first through B and then through A. If the flow rate of the water is the same as in the above problems, compare the pressures in hose A and hose B.

(a)   PA < PB
(b)   PA = PB
(c)   PA > PB

### QUESTION 22*

Suppose you float an ordinary ice-cube in a glass of ordinary water, making a mark on the side of the glass to indicate the level of the water before the ice melts. What will the level of the water will be after the ice has melted?

(a)   Slightly above the line.
(b)   Slightly below the line.
(c)   At the line (unchanged).

### QUESTION 23*

Two identical cups are filled with water to the same height. One cup is filled with ordinary water, the other cup is filled with salt water. In which cup will the top of an ice cube float the highest above the water? (Recall that the density of salt water is greater than the density of ordinary water).

(a)   Ordinary water.
(b)   Salt water.
(c)   The same.

### QUESTION 24*

A swimming pool is filled with water. The bottom of the pool is 3.5 meters below the surface of the water. If the atmospheric pressure above the pool is 1.01 x 105 Pa, what is the pressure at the bottom of the pool?

(a)   9.81 x 104 Pa
(b)   6.13 x 104 Pa
(c)   2.20 x 105 Pa
(d)   1.72 x 105 Pa
(e)   1.35 x 105 Pa

### QUESTION 25**

This and the next question are about the following situation:

Suppose you tie an aluminum block that has a volume of 0.004 m3 on the end of a string, and lower the block until it is completely submerged, hanging at rest just below the surface of the water. What is the tension T0 in the string? (The density of aluminum is 2700 kg/m3).

(a)   T0 = 39.2 N
(b)   T0 = 78.3 N
(c)   T0 = 66.7 N
(d)   T0 = 106 N
(e)   T0 = 137 N

### QUESTION 26**

Suppose the answer to the above problem is T0. If you lower the block so that it is suspended at rest just above (but not touching) the bottom of the pool, the tension in the string will be:

(a)   Greater than T0.
(b)   Less than T0.
(c)   Equal to T0.

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.