### Spring 1999 Physics 101 Hour Exam 3(22 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 true-false questions worth 2 points each, traditional multiple-choice questions worth 3 points each, and enhanced multiple-choice questions worth 6 points each. The maximum possible score is 93. When the exam was given, the minimum "A" score was 82; the minimum "B" was 70; the minimum "C" was 56; the minimum "D" was 32. The mean was 66.4; the median was 69. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

Suppose your weight on the surface of the earth is W. What would your weight be on the surface of a planet whose mass is the same as that of the earth and whose radius is twice that of the earth?

(a)   W/4
(b)   W/2
(c)   W

### QUESTION 2**

A particular neutron star has the same mass as our sun (2 x 1030 kg) but has a radius of only 10 km. Suppose a bowling ball having a mass of 7 kg is in a circular orbit of radius 50 km around this neutron star. What is the speed of the bowling ball ? (G = 6.67 x 10-11 Nm2/kg2)

(a)   2.1 x 107 m/s
(b)   6.7 x 106 m/s
(c)   8.8 x 105 m/s
(d)   3.0 x 106 m/s
(e)   5.2 x 107 m/s

### QUESTION 3**

Let the answer to the above problem be V. If the mass of the bowling ball were doubled and the radius of the orbit was unchanged, what would the speed of the ball be?

(a)   V/2
(b)   V
(c)   2V

### QUESTION 4*

If moving an object from the earth to a position 1 million miles above the earth changes its gravitational potential energy by an amount DPE, then moving the same object to a position 2 million miles above the earth would change its gravitational potential energy by an amount 2DPE.

(T)   True
(F)   False

### QUESTION 5**

Attempting to destroy an Imperial Death Star (mass M = 1020 kg, radius R = 10 km), the Rebel Alliance decides to drop a small asteroid (mass m = 109 kg) on it. Suppose the asteroid starts at rest very far away from the Death Star (r = infinity) and that the only force acting on it is gravity. How fast is the asteroid moving when it hits the death star?

(a)   1.2 x 103 m/s
(b)   7.2 x 104 m/s
(c)   4.1 x 103 m/s
(d)   6.1 x 103 m/s
(e)   9.8 x 105 m/s

### QUESTION 6**

By what factor should the Rebel Alliance increase the mass of the asteroid if they want it to have twice as much kinetic energy when it hits the Death Star?

(a)   2
(b)   4
(c)   sqrt(2)

### QUESTION 7*

A disk spinning around a fixed axis has an initial angular velocity of wi = 400 rad/s. A break is applied which slows the spinning of the disk at a constant rate of 40 rad/s2. How many turns N does the disk make between the time the break is applied and the time it stops?

(a)   N = 113
(b)   N = 752
(c)   N = 318
(d)   N = 598
(e)   N = 400

### QUESTION 8*

Suppose the answer to the above problem is N. If the initial angular velocity is doubled and the angular acceleration is kept the same, how many turns will the disk make before stopping?

(a)   2N
(b)   4N
(c)   8N

### QUESTION 9*

If the mass of the disk is M = 4 kg and the radius of the disk is R = 0.75 m, what is the net work done on the wheel as it stops? (Recall that IDISK = MR2/2.)

(a)   -3.7 x 104 J
(b)   -9.0 x 104 J
(c)   8.1 x 104 J
(d)   6.3 x 105 J
(e)   3.7 x 104 J

### QUESTION 10**

If the net force on an object is zero, then the net torque on the object about any axis is necessarily also zero.

(T)   True
(F)   False

### QUESTION 11*

A uniform horizontal beam (length L = 2 m, mass M = 3 kg) is held in static equilibrium by a hinge on a wall at one end and by a thin cable running from the other end of the beam to a point on the wall above the hinge. (See picture.) The angle between the cable and the beam is 30°. What is the tension in the cable T0?.

(a)   29.4 N
(b)   37.1 N
(c)   45.0 N
(d)   19.6 N
(e)   23.2 N

### QUESTION 12**

Let the answer to the above problem be T0. If bottom end of the cable was attached to the center of the beam rather than the end of the beam, and the angle between the cable and the beam was kept the same, how would the new tension in the cable T compare with T0?

(a)   T > T0
(b)   T = T0
(c)   T < T0

### QUESTION 13**

If the angular momentum of a system about a fixed axis is conserved then the kinetic energy of that system must also be conserved.

(T)   True
(F)   False

### QUESTION 14**

A playground merry-go-round (uniform disk with mass M = 150 kg and radius R = 2 m) rotates on a vertical frictionless axle though its center. A kid of mass m = 50 kg is riding on the merry-go-round at a distance R = 2 m from the center, and the system is initially turning with angular velocity wi = 3 rad/s. What is the kinetic energy of the kid-merry-go-round system? (Treat the kid as a point mass and recall that IDISK = MR2/2.)

(a)   2.25 x 103 J
(b)   5.50 x 103 J
(c)   1.20 x 104 J
(d)   1.35 x 103 J
(e)   7.00 x 102 J

### QUESTION 15***

In the above situation the kid now moves to the center of the merry-go-round. What is the final angular velocity wf of the system?

### QUESTION 16**

As the kid in the above problem moves toward the center of the merry-go-round, the kinetic energy of the system

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

### QUESTION 17*

An open U shaped tube is initially partially filled with water (rw = 1000 kg/m3). A 10 cm high column of oil (ro = 850 kg/m3) is carefully poured into the right side of the tube (see picture). How much higher, H, is the top of the oil on the right side than the top of the water on the left side?

(a)   0.7 cm
(b)   1.5 cm
(c)   4.1 cm
(d)   3.8 cm
(e)   2.0 cm

### QUESTION 18**

Initially, an ice-cube is floating in a glass of water. After the ice has melted, the level of the water in the glass will be:

(a)   slightly higher than the initial level
(b)   slightly lower than the initial level
(c)   the same as than the initial level

### QUESTION 19***

Initially, an ice-cube with a steel marble frozen into it is floating in a glass of water. After the ice has melted, the level of the water in the glass will be:

(a)   slightly higher than the initial level
(b)   slightly lower than the initial level
(c)   the same as than the initial level

### QUESTION 20*

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

Water (rw = 1000 kg/m3) flows though a cylindrical pipe of radius R1 = 12 cm with a speed of v1 = 2 m/s. After a narrowing of the pipe to a smaller radius R2, the speed of the water is measured to be v2 = 8 m/s.

What is the radius of the narrow part of the pipe?

(a)   R2 = 9 cm
(b)   R2 = 8 cm
(c)   R2 = 3 cm
(d)   R2 = 6 cm
(e)   R2 = 4 cm

### QUESTION 21*

What is the pressure difference DP = P1 - P2 between the wide and narrow parts of the pipe?

(a)   DP = 3.0 x 104 Pa
(b)   DP = 4.5 x 104 Pa
(c)   DP = 2.5 x 104 Pa
(d)   DP = 4.0 x 104 Pa
(e)   DP = 1.5 x 104 Pa

### QUESTION 22**

If the pipe was tilted such that the narrow end was higher than the wide end, and the speed of the water was the same as above, the pressure difference between the wide and narrow parts of the pipe would (compared to the above problem):

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

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.