### Fall 2008 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 ***.

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 111. The exam period was 90 minutes; the average score was 78.3; the median score was 81. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s2 downward and ignore any effects due to air resistance.

### QUESTION 1*

This and the following question relate to the same situation:

There is a massless rod of length 3 m. A balloon is attached at the right end B, which pulls the rod upward with a force of 105 N. At C, which is 1 m from the right end B of the rod, hangs a block of mass M. Also, a force is applied at A to keep the rod horizontal and stationary.

What is the mass M of the block?

(a)   7.2 kg
(b)   9.4 kg
(c)   11.6 kg
(d)   16.1 kg
(e)   17.3 kg

### QUESTION 2**

The torque around the axis passing through C due to the force applied at A is

(a)   positive (counterclockwise).
(b)   negative (clockwise).
(c)   not decidable due to insufficient information

### QUESTION 3**

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

A solid homogeneous cylindrical roller of mass M1 and radius 30 cm is connected via a massless pulley and with a massless wire to a block of mass M2, as shown in the figure below. M1 is 40 kg and M2 is 10 kg. The roller does not slip. The roller is placed on the slope of 30° from horizontal. At t = 0, the block M2 is going down, pulling the roller M1 along the slope -- that is, the mass M1 is climbing up the slope due to the initial push. The total kinetic energy of the system is 300 J.

What is the kinetic energy of the block M2?

(a)   31.8 J
(b)   42.9 J
(c)   54.0 J
(d)   65.1 J
(e)   76.2 J

### QUESTION 4***

What is the magnitude of the angular acceleration of the roller?

### QUESTION 5**

Suppose all the masses are doubled. The magnitude of the angular acceleration of the roller would be

(a)   unchanged.
(b)   multiplied by square root of 2.
(c)   halved.

### QUESTION 6**

This and the following question relate to the same situation:

A person is standing at the center of a rotating disk. She holds a horizontal weightless stick with two identical small masses attached to its ends, as shown in the figure.

Initially, she holds one end of the stick as in figure A.

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

### QUESTION 7**

Does she have to do positive work to pull in the stick?

(a)   yes
(b)   no
(c)   not necessarily

### QUESTION 8*

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

A cylindrical container filled with water having cross section 0.04 m2 is placed on a scale as illustrated in figure A below. The scale reads 24 kg. Now, a uniform ball is put into the container as shown in figure B. The ball floats on the water, and the reading of the scale becomes 27.3 kg. The density of water is 1000 kg/m3.

How much larger is the pressure at the bottom of the container in B than in A?

(a)   123.8 Pa
(b)   209.4 Pa
(c)   351.0 Pa
(d)   563.4 Pa
(e)   808.5 Pa

### QUESTION 9**

What is the rise of the water surface in B compared with A? (To solve this, you do not need the answer to the previous problem.)

(a)   2.5 cm
(b)   3.6 cm
(c)   5.8 cm
(d)   6.6 cm
(e)   8.3 cm

### QUESTION 10**

To immerse the ball totally under the water's surface requires a downward force of at least 13 N. What is the density of the ball?

(a)   615 kg/m3
(b)   713 kg/m3
(c)   815 kg/m3
(d)   889 kg/m3
(e)   921 kg/m3

### QUESTION 11**

Now, suppose that the ball (with the same mass) is hollow inside. The ball is cut into two halves and sinks to the bottom of the container. The height of the water surface would be

(a)   the same as in B.
(b)   lower than in B.
(c)   higher than in B.

### QUESTION 12*

A force of 10 N applied to the piston on the left side of the jack shown in the figure. This causes the working fluid inside the jack to exert a force of 1500 N on the piston on the right. The piston on the left is pushed 5 cm into the cylinder. What is the displacement of the piston on the right?

(a)   0.33 mm
(b)   0.44 mm
(c)   0.55 mm
(d)   0.66 mm
(e)   0.77 mm

### QUESTION 13*

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

Consider blood (density 1025 kg/m3) flowing through an artery with circular cross section that looks like this:

Ignore viscosity. Assume that the change in height is negligible between regions A, B, and C.

What is the mass flow rate through region A?

(a)   0.011 kg/s
(b)   0.024 kg/s
(c)   0.039 kg/s
(d)   0.052 kg/s
(e)   0.128 kg/s

### QUESTION 14**

What is the difference PB - PA in the pressure between region B and region A?

(a)   +46 Pa
(b)   +13 Pa
(c)   0 Pa
(d)   -13 Pa
(e)   -46 Pa

### QUESTION 15**

Suppose that the total pressure in region B is 230 mm/Hg (30670 Pa) above atmospheric pressure, and that a small hole in region B tears open during surgery. A narrow stream of blood rises vertically from the hole. Approximately how far above the hole will the stream rise?

(a)   0.19 m
(b)   0.38 m
(c)   0.75 m
(d)   1.5 m
(e)   3.1 m

### QUESTION 16*

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

Consider a spring with spring constant k = 30 N/m suspended vertically from a hook. A block of mass 1.0 kg is attached to the bottom of the spring.

How much longer is the spring after the mass is attached?

(a)   0.16 m
(b)   0.24 m
(c)   0.33 m

### QUESTION 17***

The block is displaced vertically downward from its equilibrium position at y = 0 to y = -6 cm and then released from rest at t = 0. Which of the following best describes the acceleration of the block?

(a)   ay = 0.06 ω2 cos ωt
(b)   ay = 0.06 ω2 sin ωt
(c)   ay = -0.06 ω2 cos ωt

### QUESTION 18*

What is the maximum speed of the block?

(a)   0.15 m/s
(b)   0.24 m/
(c)   s 0.33 m/s
(d)   1.22 m/s
(e)   2.43 m/s

### QUESTION 19*

What is the period with which the block oscillates about its equilibrium position?

(a)   0.23 s
(b)   0.49 s
(c)   1.15 s
(d)   2.30 s
(e)   5.86 s

### QUESTION 20**

Suppose the block+spring system is placed on the surface of the moon. The period calculated above would

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

### QUESTION 21*

This and the following question relate to the same situation:

The motion of the human leg during walking can be modeled (very roughly) as a simple pendulum; while one leg is on the ground, the other leg is off the ground and swinging forward with a pendulum-like motion. One period of the pendulum corresponds to two steps, and each step involves rotating the leg through a fixed angle (which is the same for everyone) about the hip.

Following this model, if you are walking next to a child who is half your height, you expect the child's walking speed to be

(a)   the same as yours.
(b)   1/sqrt(2) times yours.
(c)   1/2 of yours.

### QUESTION 22*

Following this model you would expect that, compared to the Earth, the walking speed of astronauts on the moon (g = 1.6 m/s2) is

(a)   faster.
(b)   the same.
(c)   slower.

### QUESTION 23*

A medical MRI device emits bursts of radio waves during operation. A typical frequency for these waves is 64 MHz. What is the corresponding wavelength?

(a)   1.1 m
(b)   4.7 m
(c)   5.9 m

### QUESTION 24**

A piano's middle C string vibrates at its fundamental frequency of 261.6 Hz. On one piano the total mass of the string is 0.01 kg and the length of the string is 64 cm. What is the tension in the string?

(a)   9.8 N
(b)   122 N
(c)   385 N
(d)   980 N
(e)   1752 N

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.