### Spring 2002 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. The exam period was 90 minutes; the average score was 87.0; the median score was 89. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

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

A uniform disk of unknown mass M and radius R = 10 cm is free to rotate about its axis. A light cord is wrapped around the rim on the disk and then tied to a small can of mass m = 50 gm. The cord does not slip as it unwinds on the disk. When released the can moves down with acceleration 3.27 m/s2. Take g = 9.81 m/s2.

What is the angular acceleration of the disk?

### QUESTION 2***

What is the tension in the string?

(a)   0 N
(b)   0.164 N
(c)   1.308 N
(d)   0.327 N
(e)   0.654 N

### QUESTION 3***

What is the mass of the disk?

(a)   0.8 kg
(b)   0.2 kg
(c)   0.4 kg
(d)   0.1 kg
(e)   0.6 kg

### QUESTION 4***

If the can is released from rest, the kinetic energy of the can after it has dropped a distance h is

(a)   less than mgh.
(b)   equal to mgh.
(c)   larger than mgh.

### QUESTION 5**

A uniform disk and a uniform sphere each have the same mass and radius and each roll without slipping with the same center of mass velocity on a horizontal surface. Which object has the most total kinetic energy?

(a)   The disk.
(b)   The sphere.
(c)   They both have the same total kinetic energy.

### QUESTION 6**

This and the following question relate to the same situation:

A student on a piano stool rotates freely with an angular velocity of 20 rad/s. The student holds a 1.25-kg weight in each outstretched arm, 0.759 m from the axis of rotation. The combined moment of inertia about the rotation axis of the student and stool, without the two weights, is 5.43 kg-m2, and this remains constant. Now the student pulls his arms inward to the rotation axis. What is the new angular velocity of the student?

### QUESTION 7**

The work done by the student in pulling the weights inward is

(a)   greater than zero.
(b)   less than zero.
(c)   equal to zero.

### QUESTION 8*

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

A 3 kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t) = 4cos(5t), where x is in meters and t is in seconds. What is the spring constant of the spring?

(a)   43 N/m
(b)   12 N/m
(c)   75 N/m
(d)   20 N/m
(e)   60 N/m

### QUESTION 9*

What is the maximum velocity of the block?

(a)   5 m/s
(b)   20 m/s
(c)   70 m/s
(d)   100 m/s
(e)   150 m/s

### QUESTION 10*

Now suppose the amplitude of the oscillation is doubled. How will the period of oscillation change?

(a)   The period will be doubled.
(b)   The period will be halved.
(c)   The period will be unchanged.

### QUESTION 11*

This and the following question relate to the same situation:

While waiting to get into the elevator that goes to the observation floor in the Sears Tower in Chicago, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute.

What is the length of the thread?

(a)   7 cm
(b)   11 cm
(c)   15 cm
(d)   19 cm
(e)   23 cm

### QUESTION 12**

You are now in the elevator that is accelerating upward. If you would now repeat the experiment of the previous problem, you would find that the pendulum completes

(a)   more than 90 cycles in 1 minute.
(b)   exactly 90 cycles in 1 minute.
(c)   less than 90 cycles in 1 minute.

### QUESTION 13*

This and the following question relate to the same situation:

A block of mass M = 11 kg and initial velocity v = 2.0 m/s slides on a frictionless horizontal surface and collides with a relaxed spring of spring constant k = 27 N/m. The other end of the spring is attached to a wall, as shown in the figure.

What is the maximum compression of the spring?

(a)   0.3 m
(b)   0.7 m
(c)   1.0 m
(d)   1.3 m
(e)   1.6 m

### QUESTION 14*

Let x be the answer to the previous question. If the block had a mass 4 time larger (that is, 44 kg) with the same initial velocity, the maximum compression would now be equal to:

(a)   4 x
(b)   x / 2
(c)   2 x

### QUESTION 15*

This and the following question relate to the same situation:

A raft is 4.2 m wide and 6.5 m long and it floats on water (density of water = 1000 kg/m3). When a horse is loaded onto the raft, it sinks an additional 0.027 m deeper into the water. What is the weight of the horse?

(a)   7200 N
(b)   1400 N
(c)   2400 N
(d)   9500 N
(e)   5700 N

### QUESTION 16*

What if the same horse were put on the same raft floating in salt water, which is more dense than fresh water. The raft sinks an additional amount which is

(a)   less than 0.027 m.
(b)   equal to 0.027 m.
(c)   greater than 0.027 m.

### QUESTION 17**

A hot air balloon plus its cargo has a mass of 327 kg and a volume of 687 m3. The balloon is floating at a constant height above the ground. Given that the density of the surrounding air is 1.27 kg/m3, what is the density of the hot air inside the balloon?

(a)   0.25 kg/m3
(b)   0.45 kg/m3
(c)   0.62 kg/m3
(d)   0.79 kg/m3
(e)   1.36 kg/m3

### QUESTION 18*

As a storm approaches, you notice that the column of mercury (density = 13,600 kg/m3) rises only to a height of 740 mm. What is the air pressure?

(a)   0.85 × 105 Pa
(b)   0.91 × 105 Pa
(c)   0.99 × 105 Pa
(d)   1.02 × 105 Pa
(e)   1.05 × 105 Pa

### QUESTION 19*

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

Water (density = 1000 kg/m2) flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference between the two tubes is 7.5 kPa. Which tube has the higher pressure?

(a)   the one with the larger diameter.
(b)   the one with the smaller diameter

### QUESTION 20*

Suppose the flow speed is V in the 2.8 cm diameter tube. What is the flow speed in the 1.6 cm diameter tube?

(a)   1.75 V
(b)   3.06 V
(c)   0.33 V

### QUESTION 21***

What is the flow speed V in the 2.8 cm diameter tube?

(a)   0.15 m/s
(b)   1.9 m/s
(c)   2.4 m/s
(d)   1.0 m/s
(e)   1.3 m/s

### QUESTION 22*

This and the following question relate to the same situation:

Early in the morning, when the temperature is 5.0°C, gasoline is pumped into the 51-liter steel tank of a car until it is filled to the top. Later in the day the temperature rises to 25°C. Given that the coefficient of volume expansion is 0.95 × 10-3 °C-1 for gasoline and 0.036 × 10-3 °C-1 for steel, how much gasoline spills out of the tank?

(a)   0.25 L
(b)   0.67 L
(c)   0.93 L
(d)   1.7 L
(e)   2.5 L

### QUESTION 23*

Suppose instead that the tank were made of aluminum, which has a larger volume expansion than steel. Compared to the amount of gasoline that spills out of the steel tank, the amount of gasoline that spills out of the aluminum tank is

(a)   greater.
(b)   less.
(c)   the same.

### QUESTION 24*

This and the following question relate to the same situation:

A 100 g ice cube having an initial temperature of 0°C is put into an insulated cup containing 200 g of water. After a long time, all the ice is melted and the remaining water is at 0°C. Assuming no heat flows into or out of the cup, what was the initial temperature of the water?

(a)   10°C
(b)   20°C
(c)   30°C
(d)   40°C
(e)   50°C

### QUESTION 25*

Suppose instead that the mass of the water is 300 g but everything else (that is, initial temperature of ice and water and initial mass of ice) is the same. Which of the following statements best describes the contents of the cup after a long time?

(a)   a mixture of water and ice at 0°C
(b)   a mixture of water and ice at a temperature higher than 0°C
(c)   water at a temperature higher than 0°C

### QUESTION 26**

A 2 kg block of aluminum (specific heat = 900 J/kg-°C) and a 4 kg block of steel (specific heat = 450 J/kg-°C) are both at an initial temperature of 80°C. Both are placed into identical but separate insulated buckets of water, each bucket containing 1kg of water initially at 20°C. Assuming no heat leaves the buckets, which one contains the warmest water after a long time?

(a)   The bucket with the aluminum block.
(b)   The bucket with the steel block.
(c)   Both buckets will be at the same temperature.

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.