Spring 2010 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 73.5; the median score was 75. 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*

A block of copper is placed into a large beaker of mercury and floats on top. What fraction of the copper block's volume is submerged? The density of copper is 8920 kg/m3 and that of mercury 13500 kg/m3.

(a)   0.80
(b)   0.66
(c)   0.33


QUESTION 2*

A tank of water of mass m = 100 kg is placed on a scale. A block of steel hanging from a massless string is lowered into the water, but not touching the bottom of the tank; that is, the steel is completely immersed in the water, and the steel block is held in place by the tension T of the string. The block of steel has a volume of 0.01 m3. What is the reading of the scale now with the tank of water plus the steel hanging in the water? The density of water is 1000 kg/m3.

(a)   24 kg
(b)   66 kg
(c)   110 kg
(d)   280 kg
(e)   320 kg


QUESTION 3*

A rectangular tank is filled with gasoline to a depth of 1 meter. What is the pressure difference between the top and the bottom of the tank? The density of gasoline is 750 kg/m3.

(a)   7.35 × 103 pascals
(b)   7.50 × 104 pascals
(c)   1.07 × 105 pascals


QUESTION 4*

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

A glass cylinder (closed on the bottom) is filled to a depth of 0.10 m with water. The cross section of the cylinder is 0.01 m2. The glass cylinder, filled with the water, gives a scale reading of 2 kg. A uniform ball is put into the water, and it floats. The scale reading of the glass + water + ball is now 2.1 kg. The density of water is 1000 kg/m3.

What is the pressure difference between the top and bottom of the water in the glass before the ball is inserted?

(a)   480 Nm-2
(b)   980 Nm-2
(c)   1860 Nm-2


QUESTION 5**

What is the pressure difference between the top and bottom of the water in the glass after the ball is inserted?

(a)   120 Nm-2
(b)   420 Nm-2
(c)   660 Nm-2
(d)   1078 Nm-2
(e)   1860 Nm-2


QUESTION 6**

To push the ball completely under water requires 2 N of downward force. What is the density of the ball?

(a)   120 kg/m3
(b)   329 kg/m3
(c)   660 kg/m3
(d)   1078 kg/m3
(e)   1860 kg/m3


QUESTION 7**

A block of 0.1 kg is hanging from a spring. When set in motion, the spring and the block oscillate together with a frequency of 2.5 Hz. When a second block is attached to the first block, the oscillation frequency changes to 1.5 Hz. What is the mass of the 2nd block?

(a)   0.06 kg
(b)   0.15 kg
(c)   0.18 kg


QUESTION 8*

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

A 5 kg block is hanging from a spring. The spring is supported rigidly from above. The equilibrium position of the block is where the block hangs when it is not oscillating. The block is made to oscillate such that the displacement of the block from its equilibrium position is 0.1 m. The speed of the block is measured, and it is determined that the speed of the block when it passes through the equilibrium position is 1 m/s.

What is the spring constant?

(a)   500 N/m
(b)   750 N/m
(c)   1500 N/m


QUESTION 9*

What is the approximate period of the oscillation?

(a)   0.34 s
(b)   0.43 s
(c)   0.63 s


QUESTION 10*

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

In an experiment in lab you worked with an apparatus shown in the figure. A string is attached at one end to a mechanical vibrating transducer. The other end of the string is hung over a pulley, and a weight of 0.5 kg is attached to this end of the string. The vibrating transducer causes the string to vibrate. The wavelength of the lowest frequency of vibration (the fundamental mode) is 6 m.

What is the length of the string between the transducer and the pulley?

(a)   3 m
(b)   6 m
(c)   12 m


QUESTION 11*

By adjusting the frequency of the vibrating transducer, you determine that the frequency of this fundamental mode is 10 Hz. What is the mass per unit length of the string?

(a)   1.8 × 10-5 kg/m
(b)   1.2 × 10-4 kg/m
(c)   7.4 × 10-4 kg/m
(d)   1.4 × 10-3 kg/m
(e)   2.4 × 10-3 kg/m


QUESTION 12**

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

Illustrated below is an ejector of liquid with a piston. A force F is applied to the piston and the liquid comes out of a small nozzle on the left with a high speed. The ejector is in air at ambient atmospheric pressure, which also acts on the piston. The device is horizontal. The area of the small hole at the tip of the nozzle is 10-6 m2 and the area of the piston is 10-2 m2. The liquid is assumed to be incompressible and its density is 700 kg/m3.

What is the force F you must apply on the piston to eject the liquid at a speed of 12 m/s?

(a)   504 N
(b)   605 N
(c)   706 N
(d)   807 N
(e)   908 N


QUESTION 13***

Suppose the ejector is refilled with a different liquid that is twice as dense as the previous one. The same force F is applied to the piston as in the previous problem. What is the speed of the liquid coming out of the hole? You do not need to know the answer to the last question to answer this.

(a)   6.0 m/s
(b)   8.5 m/s
(c)   10 m/s
(d)   12 m/s
(e)   15 m/s


QUESTION 14*

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

A massless spring with spring constant k = 920 N/m is attached to a wall as shown. A block of mass m = 12 kg is sliding toward the spring across a frictionless floor with a speed of 2 m/s.

After touching the spring the mass decelerates. What is the maximum displacement of the spring's right end?

(a)   7 cm
(b)   12 cm
(c)   18 cm
(d)   21 cm
(e)   23 cm


QUESTION 15**

After touching the spring, when does the magnitude of the acceleration of the mass reach its maximum for the first time?

(a)   0.971 s later
(b)   0.115 s later
(c)   0.132 s later
(d)   0.142 s later
(e)   0.179 s later


QUESTION 16**

The same experiment is performed, but the speed of the block is doubled. Now the answer to the previous problem

(a)   becomes shorter.
(b)   becomes longer.
(c)   the same.


QUESTION 17***

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

A pendulum is attached at the top of a frictionless slope that makes angle of 30° with the horizontal surface as illustrated below.

Assume that the mass does not fall off the sides of the slope.

If the angle of the slope is 90° (that is, when the pendulum is hanging vertically), its period is τ s. What is the period of the pendulum on the slope as illustrated in the figure when the angle is 30°?

(a)   2τ s
(b)   21/2τ s
(c)   τ s
(d)   τ/21/2s
(e)   τ/2 s


QUESTION 18*

Now, the mass of the pendulum is doubled. What happens to the period of the pendulum on the slope compared to the last problem?

(a)   The period does not change.
(b)   The period becomes longer.
(c)   The period becomes shorter.


QUESTION 19**

A wire is strung taut between two poles. The wire is plucked and it is determined that the wave speed is 10 m/s. The tension in the wire is then increased by 30%. By how much does the wave speed change?

(a)   -3.0 m/s
(b)   -1.4 m/s
(c)   0 m/s
(d)   +1.4 m/s
(e)   +3.0 m/s


QUESTION 20***

The displacement associated with a wave on a string has the functional form y = 0.2 cos(10 x - 4 t). What is the wave speed?

(a)   0.4 m/s
(b)   0.8 m/s
(c)   2.5 m/s
(d)   3.1 m/s
(e)   5.0 m/s


QUESTION 21***

An organ pipe is initially open at both ends. The fundamental frequency of the standing sound wave is 100 Hz. Now one end of the pipe is closed. What is the frequency of the first harmonic?

(a)   100 Hz
(b)   150 Hz
(c)   200 Hz


QUESTION 22*

The speed of sound in air is about 340 m/s. A typical frequency in a human voice is 1000 Hz. The associated wavelength is closest in size to

(a)   the width of your finger.
(b)   the width of your head.
(c)   your height.


QUESTION 23**

You are at a party standing a distance D from the loudspeaker. The music is too loud, so you move to a distance 2D from the speaker. By how much does the loudness of the music decrease?

(a)   2 dB
(b)   4 dB
(c)   6 dB
(d)   8 dB
(e)   10 dB


QUESTION 24**

The speed limit on a highway is 65 mph (1 mph = 0.448 m/s). Suppose a car carries a horn that emits an 800 Hz tone. What is the largest difference between the highest and lowest frequencies you hear as the car passes by you, supposing the car keeps within the legal limits? Assume the speed of sound is 340 m/s.

(a)   22 Hz
(b)   46 Hz
(c)   79 Hz
(d)   101 Hz
(e)   138 Hz