### Fall 2002 Physics 101 Hour Exam 3(24 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 24 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 126. The exam period was 90 minutes; the average score was 97.8; the median score was 102. Click here to see the formula sheet that came with the exam.

### QUESTION 1**

When a turning figure skater draws her outstretched arms closer to her body, she finds her rotational speed increases. This is because

(a)   her moment of inertia becomes smaller while her rotational energy is conserved.
(b)   her moment of inertia becomes smaller while energy and angular momentum are conserved.
(c)   her moment of inertia becomes smaller while her angular momentum is conserved.
(d)   both her moment of inertia and her rotational energy are conserved.
(e)   both her moment of inertia and her angular momentum are conserved.

### QUESTION 2*

A car of mass 1000 kg can accelerate with constant acceleration from 0 to 60 m/s in 8 s without ``burning rubber’’, i.e. without its wheels slipping on the pavement. The car is a front wheel drive car, so only the front two wheels are involved in accelerating the car. The wheels have negligible mass compared to the car and radius 0.4 m. What is the magnitude of the torque that the engine applies to each of the front two wheels? (Hint: remember that the car is accelerated by the action of static friction between the wheels and the pavement.)

(a)   40 N-m
(b)   440 N-m
(c)   1050 N-m
(d)   1500 N-m
(e)   1700 N-m

### QUESTION 3**

A solid sphere (I = 2MR2/5) of radius R = 0.4 m rolls without slipping up a steep hill. What initial angular velocity must the sphere have to just reach the top of a hill that is 3 m high?

### QUESTION 4*

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. Two kids, each with a mass m = 50 kg, are riding on the merry-go-round at a distance R = 2 m from the center, as shown in the figure below. 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 kids as point masses and recall that IDISK = ½ MR2.)

(a)   2.25 × 103 J
(b)   5.50 × 103 J
(c)   1.20 × 104 J
(d)   3.15 × 103 J
(e)   7.00 × 102 J

### QUESTION 5**

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

### QUESTION 6**

As the kids 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 7*

This and the following three questions relate to the same situation:

You want to make a pendulum by hanging a 0.4 kg mass by a massless string. How long should the string be if you want the pendulum to oscillate with a period of 2 s.

(a)   26 cm
(b)   42 cm
(c)   58 cm
(d)   73 cm
(e)   99 cm

### QUESTION 8**

If you displace the mass of your pendulum by 3 cm in the x direction and let it go at time t = 0, which one of the following equations will describe the time dependence of the distance of the mass from its equilibrium position?

(a)   x(t) = 3 sin(wt) cm
(b)   x(t) = 3 cos(wt) cm
(c)   x(t) = - 3 sin(wt) cm

### QUESTION 9**

Under the same conditions which one of the following equations will describe the time dependence of the velocity of the mass?

(a)   v(t) = - 3w sin(wt) cm/s
(b)   v(t) = - 3w cos(wt) cm/s
(c)   v(t) = 3w cos(wt) cm/s

### QUESTION 10**

Suppose you put your pendulum in an elevator that is accelerating downward. Its period will be

(a)   more than 2 s.
(b)   less than 2 s.
(c)   2 s.

### QUESTION 11*

A 3-kg mass oscillates on a horizontal spring with amplitude 0.08 m. Given that its maximum acceleration is 3.5 m/s2, what is the period of oscillation? Neglect friction.

(a)   1.06 s
(b)   0.95 s
(c)   1.9 s
(d)   0.14 s
(e)   6.6 s

### QUESTION 12*

This and the following question relate to the same situation:

A block of mass M = 8 kg and initial velocity v = 1.2 m/s slides on a frictionless horizontal surface and collides with a relaxed spring of unknown spring constant. The other end of the spring is attached to a wall, as shown in the figure.

If the maximum compression of the spring is 0.4m, what is the spring constant?

(a)   30 N-m
(b)   44 N-m
(c)   59 N-m
(d)   63 N-m
(e)   72 N-m

### QUESTION 13*

How long does the mass stay in contact with the spring?

(a)   0.91 s
(b)   1.05 s
(c)   1.99 s
(d)   2.17 s
(e)   3.00 s

### QUESTION 14**

A mass attached to a spring is oscillating with an amplitude of 0.02 m and total energy Etot. In terms of Etot, what is the kinetic energy of the mass when it is 0.01 m from the equilibrium position?

(a)   Etot / 4
(b)   Etot / 2
(c)   3 Etot / 4
(d)   Etot
(e)   0

### QUESTION 15*

This and the following question relate to the same situation:

A submersible Alvin is lowered from a ship into the ocean until it reaches the ocean floor at a depth of 5 km. You may assume that the density of seawater is 1000 kg/m3. You may neglect atmospheric pressure.

What is the pressure outside Alvin at the ocean floor?

(a)   4.1 × 104 Pa
(b)   1.9 × 105 Pa
(c)   7.7 × 106 Pa
(d)   4.9 × 107 Pa
(e)   9.8 × 108 Pa

### QUESTION 16*

Suppose that Alvin moves to another location and a different depth, where the pressure is 107 Pa. What is the force on Alvin’s main window, which is disk of glass 10 cm in radius?

(a)   3.1 × 105 N
(b)   3.1 × 104 N
(c)   9.8 × 104 N
(d)   4.5 × 105 N
(e)   8.7 × 103 N

### QUESTION 17*

A jeweler drops a bar of gold (density 19.3 g cm-3) into a jar that is filled to the 50 cm3 mark. The water rises to the 80 cm3 mark. What is the mass of the gold bar?

(a)   0.33 kg
(b)   0.98 kg
(c)   0.09 kg
(d)   0.93 kg
(e)   0.58 kg

### QUESTION 18**

What is the ratio of the air pressure in Denver to the air pressure at sea level? You should assume that Denver has an altitude of 1.8 km, that the density of air is a constant 1.29 kg/m3 (this is not quite true, but we will assume it here), and that the pressure at sea level is 1.01 × 105 Pa.

(a)   0.77
(b)   0.83
(c)   0.89
(d)   0.91
(e)   1.05

### QUESTION 19*

This and the following two questions relate to the same situation:

A buoy of mass 2.0 kg made of styrofoam (density 100 kg m-3) is attached by a massless line to an anchor on the bottom of the ocean. At low tide the buoy floats freely on the surface of the water (density 1000 kg m-3), but at high tide it is completely underwater.

What is the tension in the line at high tide?

(a)   177 N
(b)   188 N
(c)   198 N
(d)   200 N
(e)   981 N

### QUESTION 20***

At low tide, what fraction of the buoy’s volume lies above the water line?

(a)   0.1
(b)   0.3
(c)   0.5
(d)   0.8
(e)   0.9

### QUESTION 21**

Suppose that the buoy had the same volume but was made of wood (density 500 kg m-3) instead of styrofoam. At high tide, which of the following statements is true?

(a)   The buoyancy force on the buoy is the same.
(b)   The tension in the line is greater.
(c)   The tension in the line is the same.

### QUESTION 22*

This and the following two questions relate to the same situation:

A cylindrical garden hose has a radius of 1.5 cm, and water is passing through the hose with a speed of 0.5 m/s.

How long will it take to fill a 5 liter (0.005 m3) bucket with water?

(a)   4.3 s
(b)   9.8 s
(c)   11.3 s
(d)   14.1 s
(e)   19.0 s

### QUESTION 23*

Suppose that the hose is bent somewhere along its length, and at this location its cross-sectional area is decreased by a factor of 3. What is the speed of water flow at this location?

(a)   0.13 m/s
(b)   0.5 m/s
(c)   1.0 m/s
(d)   1.5 m/s
(e)   3.0 m/s

### QUESTION 24**

Suppose that the bent piece of hose was bent more, further decreasing its cross sectional area. If the flow rate in the hose is constant, the pressure in the hose at that point will

(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.