Fall 2010 Physics 101 Hour Exam 3
(25 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 106; the average score was 74.4; the median score was 76. The exam period was 90 minutes. 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 one relate to the same situation:

Hydraulic lifts illustrated below all use the same hydraulic oil. They all have the same input-piston cross section and the same output-plunger cross section. The plunger and the car are also identical.

Choose the correct statement about the forces required to keep the car stationary.

(a)   FA > FB > FC
(b)   FA = FB > FC
(c)   FB > FA > FC
(d)   FA > FC > FB
(e)   FA > FB = FC


QUESTION 2*

Now the oil in the hydraulic lifts above is replaced by different oil with smaller density. In which case, A, B or C, is the reduction of the force needed to maintain the car stationary the smallest?

(a)   
(b)   
(c)   


QUESTION 3*

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

There is a vertical U-shaped tube containing two distinct liquids that do not mix, as illustrated below. Their densities are ρ1 and ρ2, respectively, and the column lengths are indicated in the figure. The ends of the tube are open to the external atmosphere.

What is the relationship between ρ2 and ρ1?

(a)   ρ1 > ρ2
(b)   ρ1 < ρ2
(c)   ρ1 = ρ2


QUESTION 4**

What is the ratio ρ2 / ρ1?

(a)   ρ2 / ρ1 = h / H
(b)   ρ2 / ρ1 = h / (H + h)
(c)   ρ2 / ρ1 = (H - h) / (H + h)
(d)   ρ2 / ρ1 = H / (H + h)
(e)   ρ2 / ρ1 = H / h


QUESTION 5***

On a scale is a container with liquid of density ρl. A solid ball of density ρb is lowered into the liquid. The ball does not float, but is still maintained above the bottom of the container, as illustrated in B. The reading on the scale changes by ΔM from the initial situation shown in A.

What is the volume of the ball?

(a)   V = ΔM / (ρb - ρl)
(b)   V = ΔM / ρb
(c)   V = ΔM / ρl


QUESTION 6***

An incompressible ideal liquid is flowing in the pipe illustrated below. The ratio of the cross sections of the ends is 2 (i.e. A2 / A1 = 2), and the height difference at the ends is h. The pressure is the same at the two ends (i.e. P2 = P1). Which one of the following is true?

(a)   v22 = gh / 4
(b)   v22 = gh / 2
(c)   v22 = 2gh / 3
(d)   v22 = gh
(e)   v22 = 3gh / 2


QUESTION 7**

A mass attached to a spring with a spring constant k = 2.0 N/m is oscillating along the x axis. Its velocity at time t reads:
v(t) = 3.5 cos(2.2t) m/s
What is the maximum acceleration amax of the oscillating mass in the x direction?

(a)   amax = 6.3 m/s2
(b)   amax = 7.7 m/s2
(c)   amax = 9.8 m/s2
(d)   amax = 11.3 m/s2
(e)   amax = 16.9 m/s2


QUESTION 8**

An ideal horizontal spring on a frictionless table is fixed at one end (see diagram). The other end is attached a mass M. When a horizontal force of F is applied to the mass, it is displaced by distance A from its equilibrium position. Then, the force is turned off. What is the maximum speed V of the mass?

(a)   V2 = 2A2 / F
(b)   V2 = AF / 2M
(c)   V2 = AF / M


QUESTION 9**

A pendulum made from an ideal string of length L and a mass M is hung from the ceiling. It is undergoing very small oscillations with angular amplitude θ (in radians) and period P. M, L and θ are all doubled. What is the new period of oscillation?

(a)   0.5 P
(b)   0.7 P
(c)   P
(d)   1.4 P
(e)   2 P


QUESTION 10**

Consider two containers with the same volume, each containing the same mass of gas. One is filled with water vapor (each molecule has an atomic weight of about 18), the other with nitrogen (each molecule has an atomic weight of about 28). Which has the larger number density?

(a)   water vapor
(b)   nitrogen
(c)   Not enough information is given.


QUESTION 11*

A container of hydrogen gas (atomic weight 2) at atmospheric pressure and temperature (290 K) has a volume of 1 m3. What is the mass of gas inside the container?

(a)   4.0 g
(b)   12 g
(c)   26 g
(d)   41 g
(e)   83 g


QUESTION 12*

Consider a sealed container at constant temperature containing 8 moles of hydrogen gas. If the volume of the container is increased by a factor of 2, what happens to the pressure?

(a)   It increases by a factor of 2.
(b)   It decreases by a factor of 2.
(c)   It stays the same.


QUESTION 13*

In a container of oxygen gas (mass = 32 atomic mass units) the root- mean-square speed of the molecules is 400 m/s. What is the temperature?

(a)   185 K
(b)   190 K
(c)   205 K
(d)   220 K
(e)   230 K


QUESTION 14*

The temperature in Champaign-Urbana last reached a record low of -25° F in January 1999. What is this temperature in K?

(a)   231 K
(b)   236 K
(c)   241 K


QUESTION 15**

Polyethylene has a large coefficient of volume expansion, β = 200 × 10-6 K-1. Suppose a warm (30° C) piece of polyethylene is thrown into a large vat of water at 1° C. As the polyethylene cools, will it float higher or lower in the water? At all relevant temperatures, polyethylene floats.

(a)   higher
(b)   lower
(c)   Not enough information is given.


QUESTION 16*

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

A low C (sub-contra C, or C0) has a frequency of 16.35 Hz. If you wanted to produce this note with the fundamental of an organ pipe that was open at both ends, how long would you have to make the pipe? Assume the speed of sound is 340 m/s.

(a)   3 m
(b)   5.4 m
(c)   6.6 m
(d)   9.2 m
(e)   10.4 m


QUESTION 17**

If you were to close one end of the organ pipe, would you have to make the pipe longer or shorter to produce the same frequency?

(a)   longer
(b)   shorter


QUESTION 18*

You want to produce a 16.35 Hz note from the fundamental on a 3 meter string with mass per unit length of 10-3 kg/m. What should the tension in the string be?

(a)   2.8 N
(b)   4.9 N
(c)   9.6 N
(d)   17.6 N
(e)   33.1 N


QUESTION 19**

Suppose you are standing a certain distance D from a loudspeaker, and using a digital loudness meter, you measure a certain loudness Q dB. At what distance will the loudness drop off by 10 dB?

(a)   2D
(b)   3.2D
(c)   10D


QUESTION 20*

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

A heavy ball with a hole drilled straight through it is dropped from a platform 20 m above the ground. You are standing almost (but not quite!) under the ball. The hole acts as a whistle and produces a note at 1700 Hz if you were to blow over the hole when the ball was at rest. As the ball falls toward you, the frequency you hear is

(a)   < 1700 Hz and decreasing.
(b)   < 1700 Hz and constant.
(c)   1700 Hz.
(d)   > 1700 Hz and constant.
(e)   > 1700 Hz and increasing


QUESTION 21**

Suppose the ball falls past you at 20 m/s. Just after it passes you, and is moving directly away from you, what frequency do you hear? Assume the speed of sound is 340 m/s.

(a)   1900 Hz
(b)   1800 Hz
(c)   1700 Hz
(d)   1600 Hz
(e)   1500 Hz


QUESTION 22***

A harmonic wave is excited on a string with the form:
0.01 cos(200t-30x)
Here the amplitude is measured in meters, the time in seconds, and the position x in meters. What is the wavelength of the wave?

(a)   15 cm
(b)   21 cm
(c)   31 cm


QUESTION 23*

When you blew on a pipe to make some sound, one end was open. Despite this, there was some reflection between the open end of the instrument and the surrounding air.

(T)   True
(F)   False


QUESTION 24**

A spring with a mass M on its end is undergoing simple harmonic motion. Which one of the following is false?

(a)   Its frequency is dependent on the mass M.
(b)   Its frequency is dependent on what the spring is made of.
(c)   The amplitude of motion is dependent on the mass.


QUESTION 25**

A mass is bobbing up and down on a spring as shown. Its displacement from the equilibrium position vs. time looks like:

Which of the following (a or b or c) is correct for the velocity (v), acceleration (a) and force (F)?

(a)   
(b)   
(c)