### Spring 2003 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 108. The exam period was 90 minutes; the average score was 92.9; the median score was 96. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

This and the following question relate to the same situation:

A solid cylinder of mass 2 kg and radius 10 cm rotates with a constant angular velocity of 2 rad/s about a fixed axis passing through its center. What is the rotational kinetic energy of the cylinder?

(a)   0.005 J
(b)   0.01 J
(c)   0.02 J
(d)   0.05 J
(e)   0.1 J

### QUESTION 2**

Two solid cylinders have the same mass and radii, and are released at the same time at the top of a ramp. Cylinder 1 rolls down the ramp without slipping. Cylinder 2 slides down the ramp without friction. Which one of the two cylinders reaches the bottom of the ramp first?

(a)   Cylinder 1.
(b)   Cylinder 2.
(c)   Both get to the bottom at the same time.

### QUESTION 3*

This and the following question relate to the same situation:

A ramp is 2 m long and makes an angle of 30° with respect to horizontal. A hollow cylinder is released from rest at the top of the ramp, and rolls to the bottom without slipping. As the cylinder rolls, compare the magnitude of its translational kinetic energy, KETRANS, to the magnitude of its rotational kinetic energy, KEROT.

(a)   KETRANS  >  KEROT
(b)   KETRANS  <  KEROT
(c)   KETRANS  =  KEROT

### QUESTION 4**

What is the velocity of the center of mass of the hollow cylinder at the bottom of the ramp?

(a)   0.7 m/s
(b)   1.3 m/s
(c)   2.4 m/s
(d)   3.1 m/s
(e)   4.9 m/s

### QUESTION 5*

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

A circular merry-go-round of mass 200 kg and 2 m radius rotates freely with an initial angular velocity of 0.5 rad/s about a vertical axis passing through its center. A 50 kg student is initially standing on the rim of the merry-go-round. Treat the merry-go-round as a solid disk and the student as a point particle.

What is the magnitude of the angular momentum of the student plus merry-go-round?

(a)   100 kg-m2/s
(b)   200 kg-m2/s
(c)   300 kg-m2/s
(d)   400 kg-m2/s
(e)   500 kg-m2/s

### QUESTION 6**

The student now moves toward the center of the merry-go-round. When she reaches the center, what is the angular velocity of the merry-go-round?

### QUESTION 7*

Which of the following best describes what is conserved as the student walks from the rim of the merry-go-round to the center?

(a)   Only the angular momentum of the system is conserved.
(b)   Only the kinetic energy of the system is conserved.
(c)   Both the angular momentum and the kinetic energy is conserved.

### QUESTION 8*

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

A block of mass 2.0 kg is resting on a horizontal frictionless surface and is attached to a spring with force constant k = 150 N/m. The other end of the spring is fixed to a wall. The block is located at x = 0 when the spring is relaxed.

A force of 200 N is applied to the block in the x-direction, stretching the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate back and forth along the x-axis.

What is the amplitude of the oscillation?

(a)   0.5 m
(b)   0.7 m
(c)   1.0 m
(d)   1.3 m
(e)   2.0 m

### QUESTION 9*

About how many oscillations does the block undergo in a time of 10 seconds?

(a)   14
(b)   52
(c)   67
(d)   95
(e)   110

### QUESTION 10*

Which function best describes the position of the block in the above experiment as a function of time?

(a)   x(t) = A sin(ωt)
(b)   x(t) = A cos(ωt)
(c)   x(t) = A tan(ωt)

### QUESTION 11*

Suppose the period of the oscillation in the above experiment is T0. Now suppose you repeat the experiment, but you use an initial force which is twice as big (i.e. F = 400 N) to stretch the spring. The new period of oscillation, Tnew, will be:

(a)   Tnew  =  T0
(b)   Tnew  =  2 T0
(c)   Tnew  =  T0 / 2

### QUESTION 12*

This and the following question relate to the same situation:

A pendulum is made by hanging a 0.5 kg mass from a massless string. The pendulum oscillates with simple harmonic motion with an angular velocity of ω0 = 1 rad/s. How long is the string?

(a)   2.75 m
(b)   4.14 m
(c)   6.54 m
(d)   8.91 m
(e)   9.81 m

### QUESTION 13*

Now suppose you put the above pendulum on a planet where the force of gravity acting on the mass is four times as big as it is on the earth. What is the angular velocity of the pendulum on this planet?

### QUESTION 14*

This and the following question relate to the same situation:

A 2.4 kg object is attached to one end of a spring with force constant k = 9000 N/m, and the other end of the spring is fixed. You pull the mass so that the spring is stretched 0.1 m from equilibrium, and then let go so that the mass starts oscillating back and forth. You can ignore gravity and friction.

What is the total mechanical energy of the system after you let go of the mass?

(a)   22.5 J
(b)   9 J
(c)   5 J
(d)   90 J
(e)   45 J

### QUESTION 15*

Suppose the correct answer to the above question is Etot. If the mass of the object is now doubled but the amplitude of the oscillation is kept the same, what is the new total energy of the system Enew?

(a)   Enew  =  2 Etot
(b)   Enew  =  Etot / 2
(c)   Enew  =  Etot

### QUESTION 16*

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

A block of wood has a mass of 25 kg and a volume of 0.04 m3. This block of wood (which would normally float on the surface) is held under water by a string tied to the bottom of the pool. The density of the water in the pool is 1000 kg/m3.

What is the magnitude of the buoyant force acting on the block?

(a)   98 N
(b)   147 N
(c)   245 N
(d)   392 N
(e)   517 N

### QUESTION 17*

What is the tension in the string T?

(a)   98 N
(b)   147 N
(c)   245 N
(d)   392 N
(e)   517 N

### QUESTION 18**

Now suppose the string is cut and the block floats on the surface on the water. The magnitude of the bouyant force on the block is now

(a)   equal to the weight of the block.
(b)   greater than the weight of the block.
(c)   less than the weight of the block.

### QUESTION 19*

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

Hose A has an inner radius of 2 cm and water flows through it with a speed of 50 m/s. Hose A is attached hose B, which has a larger inner radius. The speed of the water in hose B is measured to be 2 m/s.

What is the inner radius of hose B?

(a)   1 cm
(b)   4 cm
(c)   6 cm
(d)   8 cm
(e)   10 cm

### QUESTION 20*

PA is the pressure in hose A and PB is the pressure in hose B. Which one of the following statements is true?

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

### 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, now compare the pressures in hose A and hose B.

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

### QUESTION 22*

Bucket A contains pure water. Bucket B contains salt water (which has a higher density than pure water). An identical ball is placed in each bucket. The ball in bucket A floats with exactly half of its volume under water. How much of the volume of the ball in bucket B is under water?

(a)   Exactly half of the ball in bucket B is under water.
(b)   More than half of the ball in bucket B is under water.
(c)   Less than half of the ball in bucket B is under water.

### QUESTION 23*

An aluminum plate has a circular hole cut in it. When the temperature of the plate is lowered, the diameter of the hole

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

### QUESTION 24*

A 1 kg block of ice is floating in a tub containing 1 kg of water. The initial temperature of both the ice and the water is 0°C. How much heat must be added to the system to melt all of the ice and raise the temperature of the water in the tub to 100°C? (The specific heat capacity of water is 4186 J/kg-°C, and the latent heat of fusion of water is 335000 J/kg.)

(a)   1.2 × 106 J
(b)   1.7 × 106 J
(c)   2.2 × 106 J
(d)   2.7 × 106 J
(e)   3.2 × 106 J

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.