### Spring 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 116. The exam period was 90 minutes; the average score was 83.9; the median score was 86. Click here to see page1 page2 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 four questions relate to the same situation:

A 3 kg mass attached to a spring sits at rest at its equilibrium position, as shown. At time t = 0 the mass is set in motion to the left with an initial velocity of 3.3 m/s. The angular frequency of this harmonic oscillator is ω = 4.2 rad/s.

How long does it take for the mass to complete one full cycle of its motion?

(a)   0.5 s
(b)   1 s
(c)   1.5 s

### QUESTION 2**

Which equation best describes the velocity of the mass as a function of time, v(t)?

(a)   v(t) = - 3.3 cos(4.2 t)
(b)   v(t) = 4.2 cos(3.3 t)
(c)   v(t) = 4.2 sin(3.3 t)
(d)   v(t) = - 3.3 sin(4.2 t)
(e)   v(t) = - 4.2 cos(3.3 t)

### QUESTION 3*

What is the force constant k of the spring?

(a)   28 N/m
(b)   53 N/m
(c)   84 N/m

### QUESTION 4*

What is the maximum distance xmax that the mass gets displaced from its equilibrium position during one cycle of its motion?

(a)   0.218 m
(b)   0.366 m
(c)   0.524 m
(d)   0.786 m
(e)   0.956 m

### QUESTION 5*

What is the total energy of the system?

(a)   16.3 J
(b)   25.8 J
(c)   42.6 J
(d)   55.9 J
(e)   72.1 J

### QUESTION 6*

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

A string is stretched between a transducer and a support. It is held in tension by a mass hanging off one end. The length of the string L = 0.8 m and its mass density μ = 0.2 kg/m. The transducer excites a standing wave on the string as shown in the figure.

Is this wave transverse or longitudinal?

(a)   transverse
(b)   longitudinal

### QUESTION 7*

The speed of sound on the string is determined to be v = 42 m/s. What is the mass m of the weight?

(a)   9 kg
(b)   18 kg
(c)   24 kg
(d)   36 kg
(e)   44 kg

### QUESTION 8*

What is the frequency f of the oscillation of the string?

(a)   55 Hz
(b)   63 Hz
(c)   78 Hz
(d)   92 Hz
(e)   105 Hz

### QUESTION 9*

A grandfather clock keeps time by counting the cycles of a pendulum, whose period is 2 sec. How long must the pendulum be?

(a)   0.26 m
(b)   0.44 m
(c)   0.63 m
(d)   0.87 m
(e)   1 m

### QUESTION 10*

This and the following question relate to the same situation:

You are trying to study but your roommate is blasting his stereo so loud you cannot think. You are standing a distance 3 m away and measure the intensity of the sound to be I = 3.98 W/m2.

What is the loudness of the sound?

(a)   105 dB
(b)   112 dB
(c)   119 dB
(d)   126 dB
(e)   131 dB

### QUESTION 11**

You cannot study if the intensity is greater than 0.8 W/m2. What is the minimum distance to which you must move from the stereo? (Assume there are no obstacles you can hide behind and you have no ear plugs.)

(a)   3.86 m
(b)   4.02 m
(c)   6.69 m
(d)   12.8 m
(e)   25.4 m

### QUESTION 12*

This and the following question relate to the same situation:

You are standing at a street corner listening to a fire engine, which is approaching you at a speed of 60 mph (26.8 m/s). The fire engine sounds its siren with a frequency f = 460 Hz. The speed of sound in air is 343 m/s.

At what frequency do you hear the siren?

(a)   436 Hz
(b)   460 Hz
(c)   499 Hz
(d)   514 Hz
(e)   554 Hz

### QUESTION 13*

The ambulance passes you and is now traveling away from you at the same speed. What is frequency you hear now?

(a)   405 Hz
(b)   427 Hz
(c)   448 Hz
(d)   460 Hz
(e)   477 Hz

### QUESTION 14*

A patient is being given an intraveneous drip. The vertical distance from the top of the fluid to the patient's arm is 1.5 m. The fluid in the bag has density of 1000 kg/m3 and is at atmospheric pressure (105 Pa). What is the pressure of the fluid at the patient's arm?

(a)   100000 N/m2
(b)   106940 N/m2
(c)   114700 N/m2

### QUESTION 15**

A laboratory building is being constructed under water. The building has mass 50,000 kg and volume 300 m3. What is the force acting on the building? The upward direction is assumed positive. The density of water is 1000 kg/m3. (Hint: include only the buoyant force and the gravity force into your calculation.)

(a)   -2.45 × 106 N
(b)   -4.9 × 105 N
(c)   4.9 × 105 N
(d)   2.45 × 106 N
(e)   2.94 × 106 N

### QUESTION 16*

A rubber duck floats in water (the water density is 1000 kg/m3). One fifth of the volume of the rubber duck is below the surface of the water. What is the density of the rubber duck?

(a)   200 kg/m3
(b)   300 kg/m3
(c)   400 kg/m3

### QUESTION 17***

A faucet runs water. The cross-section of the opening in the faucet has area 1 cm2. 10 cm below the faucet the cross-section of the stream of water has thinned to 0.4 cm2. What is the speed at which the water exits the faucet?

(a)   29 cm/s
(b)   42 cm/s
(c)   61 cm/s
(d)   83 cm/s
(e)   101 cm/s

### QUESTION 18**

This and the following question relate to the same situation:

A cylindrically shaped peg sits in a cup, as shown in the figure. You are asked to remove the peg without touching it. Remembering physics 101, you blow air across the top of the peg. The radius R of the peg is 0.02 m, and its mass is 0.01 kg. The density of air is 1.29 kg/m3.

What is the minimum speed vair required to lift the peg?

(a)   7 m/s
(b)   9 m/s
(c)   11 m/s

### QUESTION 19***

If R were increased, while the density of the peg remained unchanged, what would happen to the required value of vair?

(a)   It would be smaller.
(b)   It would be the same.
(c)   It would be bigger.

### QUESTION 20**

This and the following question relate to the same situation:

You are pushing water out of a syringe (the density of water is ρ = 1000 kg/m3). The radius of the piston is 0.005 m, the radius of the needle is 0.001 m. The water exits the opening at 10 m/s. What force F are you applying to the piston of the syringe?

(a)   F = 1.1 N
(b)   F = 1.4 N
(c)   F = 2.6 N
(d)   F = 3.3 N
(e)   F = 3.9 N

### QUESTION 21**

Suppose the syringe were filled with alcohol instead of water. Alcohol has lower density than water. If the force on the piston were still the same, would the alcohol come out faster or slower than the water does?

(a)   faster
(b)   slower
(c)   unchanged

### QUESTION 22***

This and the following question relate to the same situation:

A ball of mass 12 kg is dropped onto a vertical, massless spring with spring constant k = 2000 N/m. The ball sticks to the spring and compresses the spring by as much as 0.2 m. What was the speed of the ball at the moment when it hit the top of the spring? Assume no energy was lost in the collision. (Hint: the gravitational potential energy of the ball changes as the spring is compressed).

(a)   0.757 m/s
(b)   0.957 m/s
(c)   1.257 m/s
(d)   1.657 m/s
(e)   1.957 m/s

### QUESTION 23*

After the first compression, the mass oscillates up and down. What is the frequency of this oscillation?

(a)   1.75 Hz
(b)   2.05 Hz
(c)   2.40 Hz
(d)   2.85 Hz
(e)   3.15 Hz

### QUESTION 24***

A spring has spring constant k. If it is cut in half, how does the spring constant of each piece compares to that of the original spring? (Hint: think about Hooke's law).

(a)   It would be bigger.
(b)   It would be the same.
(c)   It would be smaller.

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.
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