### Spring 2009 Physics 101 Hour Exam 3(23 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 120. The exam period was 90 minutes; the average score was 93.3; the median score was 98. 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 question and the following three relate to the same situation:

A piston of area A = 0.3 m2 sits on top the water in a tank (ρ = 1000 kg/m3), in which a block of mass m = 0.2 kg that is tethered by a string floats. Ssee figure.

Another mass M = 30 kg is placed on top of the piston. By how much does the pressure increase at the position marked X?

(a)   980 Pa
(b)   1100 Pa
(c)   1730 Pa
(d)   2000 Pa
(e)   5010 Pa

### QUESTION 2**

Compared to the magnitude of the buoyant force on the floating mass, the tension in the string has

(a)   smaller magnitude.
(b)   the same magnitude.
(c)   greater magnitude.

### QUESTION 3**

Suppose the tension in the string is T = 0.5 N. What is the density of the floating mass m?

(a)   344 kg/m3
(b)   419 kg/m3
(c)   501 kg/m3
(d)   699 kg/m3
(e)   797 kg/m3

### QUESTION 4*

Suppose the water in the tank is 1.3 m deep. How much greater is the pressure at the bottom than at the top?

(a)   980 Pa
(b)   1402 Pa
(c)   3870 Pa
(d)   8880 Pa
(e)   12740 Pa

### QUESTION 5*

A string of mass density μ = 3 × 10-4 kg/m is stretched between two fixed points which are 1.7 m apart. If the fundamental frequency is 330 Hz, what is the tension in the string?

(a)   39 N
(b)   120 N
(c)   190 N
(d)   250 N
(e)   380 N

### QUESTION 6*

The electronic tags used in high tech libraries to locate books use microwaves of frequency 2.45 GHz (1 GHz = 109 Hz). What is the wavelength of this microwave?

(a)   0.6 cm
(b)   1.2 cm
(c)   6.0 cm
(d)   12 cm
(e)   21 cm

### QUESTION 7**

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

Oil (density = 800 kg/m3) flows through a cylindrical pipe, then through a narrower valve with circular cross section, and finally emerges into an open, cylindrical tank of radius 15 m where the pressure is 105 Pa (i.e. equals atmospheric pressure). See diagram. The speed of fluid in the pipe is 1.59 m/s. The speed of fluid in the valve is 25.5 m/s.

What is the ratio of the radius rp of the pipe to the radius rv of the valve?

(a)   rp / rv = 4
(b)   rp / rv = 2
(c)   rp / rv = 1
(d)   rp / rv = 0.5
(e)   rp / rv = 0.063

### QUESTION 8*

If Fp is the volume flow rate in the pipe and Fv is the volume flow rate in the valve, which one of the following is true?

(a)   Fp > Fv
(b)   Fp = Fv
(c)   Fp < Fv

### QUESTION 9**

Suppose it takes 1 hour to fill the tank to a depth of 1 m. What is the radius of the valve?

(a)   0.01 m
(b)   0.05 m
(c)   0.2 m
(d)   0.8 m
(e)   1.6 m

### QUESTION 10**

What is the pressure in the pipe? (Hint: the pressure just outside the valve is equal to atmospheric pressure.)

(a)   240000 Pa
(b)   360000 Pa
(c)   480000 Pa
(d)   600000 Pa
(e)   720000 Pa

### QUESTION 11*

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

A mass M = 2 kg is suspended by a spring with spring constant k = 8 N/m. Initially the mass is at its resting position, y = 0. At t = 0 it is struck sharply from below by a hammer so that the mass begins to move with speed 0.1 m/s.

What is the period with which the mass oscillates?

(a)   1.1 s
(b)   2.1 s
(c)   3.1 s
(d)   4.1 s
(e)   5.1 s

### QUESTION 12*

Suppose the setup was placed on the moon (where the gravitational acceleration is smaller than for Earth); the period of oscillation would be

(a)   smaller.
(b)   larger.
(c)   the same.

### QUESTION 13**

Which of the following equations best describes the position of the mass?

(a)   y = 0.05 sin(2t) m
(b)   y = 0.05 cos(2t) m
(c)   y = 0.1 sin(2t) m
(d)   y = 0.1 cos(2t) m
(e)   y = 0.1 cos(4t) m

### QUESTION 14**

What is the maximum acceleration of the mass?

(a)   0.1 m/s2
(b)   0.2 m/s2
(c)   0.3 m/s2
(d)   0.4 m/s2
(e)   0.5 m/s2

### QUESTION 15*

This and the following question relate to the same situation:

A spring with a block of mass 3.8 kg attached at one end is fixed to the wall. A leftward force of F = 35 N is applied on the mass, compressing the spring (Fig. A). The mass is then released with zero initial velocity and starts to oscillate (Fig. B). The spring constant is k = 150 N/m.

What is the maximum kinetic energy of the mass?

(a)   4 J
(b)   8 J
(c)   10 J
(d)   11 J
(e)   15 J

### QUESTION 16*

Now suppose the force F is doubled. How does the period of the oscillation change?

(a)   It is halved.
(b)   It is doubled.
(c)   It remains the same.

### QUESTION 17**

This and the following question relate to the same situation:

A pendulum consists of a point mass M = 7.3 kg suspended at the end of a string of length L = 1.3 m.

The maximum speed of the point mass is v = 0.75 m/s. What is the difference in the height Δh of the mass between its highest and lowest positions while oscillating?

(a)   Δh = 1.2 cm
(b)   Δh = 2.1 cm
(c)   Δh = 2.9 cm
(d)   Δh = 3.7 cm
(e)   Δh = 4.1 cm

### QUESTION 18*

What is the period of the pendulum?

(a)   1.2 s
(b)   2.3 s
(c)   3.4 s
(d)   4.5 s
(e)   5.6

### QUESTION 19*

This and the following question relate to the same situation:

A sound wave with frequency 520 Hz hits a balloon containing a mixture of gases. Inside the balloon the wavelength is increased by 30% compared with that in the air (in which the sound speed is 340 m/s).

What is the speed of sound inside the balloon?

(a)   200 m/s
(b)   260 m/s
(c)   340 m/s
(d)   440 m/s
(e)   570 m/s

### QUESTION 20*

What is the frequency of the sound wave inside the balloon?

(a)   400 Hz
(b)   520 Hz
(c)   680 Hz

### QUESTION 21**

Jet planes A and B are flying along the same flight-path at speed cs/2, where cs is the speed of sound (see diagram). Each has an engine that emits sound at a frequency f (as heard by the pilot on each plane). An observer on the ground between the two planes hears frequencies fA and fB.

What is the ratio of the frequencies (where fA is from plane A and fB is from plane B)?

(a)   fB / fA = 1/9
(b)   fB / fA = 1/3
(c)   fB / fA = 1
(d)   fB / fA = 3
(e)   fB / fA = 9

### QUESTION 22*

The loudness of a trumpet at distance 10 m is 80 dB.

How many trumpeters at distance 10 m must play in unison to increase the loudness to 100 dB?

(a)   10 players
(b)   20 players
(c)   50 players
(d)   100 players
(e)   200 players

### QUESTION 23*

You ask all the players to recede by 20 m so that all the players to be 30 m away from you. What is the ratio of the new intensity to the old intensity?

(a)   0.5
(b)   0.33
(c)   0.11

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.