### Fall 2007 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 113. The exam period was 90 minutes; the average score was 74.1; the median score was 74. 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**

Fluids A and B are poured into a U-shaped pipe, shown below. Fluid A is water (ρ = 1000 kg/m3). It rises 0.3 m above the bottom of the left pipe, and 0. 1 m above the bottom of the right pipe. Fluid B of density (ρB = 500 kg/m3) in the right pipe rises height h above the level of water. (The drawing is not to scale.)

Calculate h.

(a)   0.2 m
(b)   0.4 m
(c)   0.6 m
(d)   0.8 m
(e)   1.0 m

### QUESTION 2**

Two organ pipes are open at both ends and are excited at their fundamental (i.e. lowest) frequency. Pipe A has length LA = 3.5 m and pipe B has length LB = 3.4 m. Pipe A is held at a constant temperature T = 23°C. At what temperature must pipe B be held so that the two pipes generate the same frequency? You may neglect the change in length of the pipe. The speed of sound is v = 331 m/s + (0.6m/s/°C) T, where T is measured in °C.

(a)   3.5 °C
(b)   6.6 °C
(c)   15.4 °C
(d)   24.8 °C
(e)   34.5 °C

### QUESTION 3***

This and the following question relate to the same situation:

When a block of iron of mass 39.30 kg is suspended from a spring with spring constant 500 N/m, the length of the spring is 4.7 m.

A tub of water is placed so that the iron is completely submerged in the water. What is the length of the spring now? (The drawing is not to scale.)

Density of iron: ρiron = 7860 kg/m3
Density of water: ρwater = 1000 kg/m3

(a)   3.2 m
(b)   3.7 m
(c)   4.1 m
(d)   4.6 m
(e)   4.7 m

### QUESTION 4*

Next, the iron block is detached from the spring and water is replaced with mercury (density ρmercury = 13500kg/m3). What fraction of the iron block will be submerged in mercury?

(a)   Vsubmerged / Vtotal = 0.48
(b)   Vsubmerged / Vtotal = 0.58
(c)   Vsubmerged / Vtotal = 0.65

### QUESTION 5*

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

A 2 kg pendulum is placed on an elevator next to a 2 kg mass hung vertically by a spring with spring constant 200 N/m. When the elevator is at rest, the spring oscillates twice as fast as the pendulum: 0.5 Tpendulum = Tmass on spring.

What is the length of the pendulum?

(a)   8.9 cm
(b)   15.1 cm
(c)   23.2 cm
(d)   39.2 cm
(e)   42.5 cm

### QUESTION 6**

The equilibrium length of the spring with the 2 kg mass attached when the elevator is at rest is 1.2 m. What is the length of the relaxed spring without the mass attached to it?

(a)   0.98 m
(b)   1.03 m
(c)   1.10 m

### QUESTION 7**

The mass on the spring oscillates with the amplitude 0.3 m. What is the speed of the mass when it is 0.2 meters from its equilibrium position?

(a)   2.1 m/s
(b)   2.2 m/s
(c)   2.7 m/s
(d)   3.1 m/s
(e)   3.8 m/s

### QUESTION 8**

The elevator now accelerates downward with constant acceleration a = 2.5 m/s2.

Compare 0.5 Tpendulum, half the period of the pendulum, to Tmass on spring, the frequency of the mass on the spring when the elevator is accelerating down.

(a)   0.5 Tpendulum < Tmass on spring
(b)   0.5 Tpendulum = Tmass on spring
(c)   0.5 Tpendulum > Tmass on spring

### QUESTION 9*

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

A block of mass 2.0 kg resting on a horizontal frictionless surface is attached to a spring with spring constant k. A force F is applied to the block in the +x direction compressing the spring. After the spring compresses 0.1 m, at time t = 0, the force is removed and the block on the spring starts to oscillate with angular frequency ω = 11/s.

What is the magnitude of the spring constant k?

(a)   207 N/m
(b)   220 N/m
(c)   242 N/m

### QUESTION 10**

At which of these three stages is the magnitude of the acceleration the greatest?

(a)   when the spring is at its relaxed length
(b)   when the spring is at its minimum length
(c)   when the spring's length is half way between its relaxed length and its minimum length

### QUESTION 11*

The displacement of the mass from the equilibrium position is described by the expression:

(a)   Δx = 11 cos(11t)
(b)   Δx = 0.1 sin (11t)
(c)   Δx = 0.1 cos(0.1t)
(d)   Δx = 0.1 cos(11t)
(e)   Δx = 11 sin(11t)

### QUESTION 12*

This and the following question relate to the same situation:

A hydraulic lift is filled with oil (ρ = 600 kg/m3). The cross section area of the large piston in the cylinder on the right is A2 = 170 cm2. The area of the small piston in the cylinder on the left is A1 = 0.5 cm2.

Force F1 = 50 N needs to be applied to the small piston to lift weight W2 on the right so the bottom of both pistons is at the same height. What is the magnitude of the weight W2?

(a)   W2 = 1700 N
(b)   W2 = 17000 N
(c)   W2 = 170000 N

### QUESTION 13*

How far do we have to push down the small piston for the load on the right to go up 0.03 cm?

(a)   5.5 cm
(b)   7.5 cm
(c)   10.2 cm

### QUESTION 14*

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

Water flows through the pipe as shown below. Segment 1 has a cross sectional area A1 = 20 cm2. Segment 2 has the same cross section but its center (indicated by the dashed line) is h = 0.11 m lower. Finally, the water flows into a narrower Segment 3 with a cross sectional area A3. The center of pipe in Segments 2 and 3 is at the same height, as indicated by the dashed line. The velocity of water in Segment 1 is v1 = 0.3 m/s, and in Segment 3 it is v3 = 3 m/s. The density of water is 1000 kg/m3. Note: the drawing not to scale.

What is the cross section A3 of the narrow pipe?

(a)   A3 = 2.00 cm2
(b)   A3 = 2.75 cm2
(c)   A3 = 3.00 cm2

### QUESTION 15**

Define P1 = the water pressure Segment 1, P2 = the water pressure in Segment 2, and P3 = the water pressure in Segment 3.

Which statement is correct about pressure P1 and P2?

(a)   P1 < P2
(b)   P1 = P2
(c)   P1 > P2

### QUESTION 16**

What is the absolute value of the water pressure difference, | ΔP12 |  =  | P1 - P2 | ?

(a)   | ΔP12 |  =  0
(b)   | ΔP12 |  =  245 Pa
(c)   | ΔP12 |  =  490 Pa
(d)   | ΔP12 |  =  980 Pa
(e)   | ΔP12 |  =  1078 Pa

### QUESTION 17*

Which statement is correct about pressure P2 and P3?

(a)   P2 < P3
(b)   P2 = P3
(c)   P2 > P3

### QUESTION 18**

What is the absolute value of the water pressure difference, | ΔP23 |  =  | P2 P3 | between Segments 2 and Segment 3 of the pipe?

(a)   | ΔP23 | = 0
(b)   | ΔP23 | = 1230 Pa
(c)   | ΔP23 | = 2450 Pa
(d)   | ΔP23 | = 4455 Pa
(e)   | ΔP23 | = 6980 Pa

### QUESTION 19**

This and the following question relate to the same situation:

One end of a string with length L = 2 m and mass density μ is attached to a weight with mass 4.3 kg. The other end of the string is fixed to a transducer that vibrates at a frequency of 212 Hz. A standing wave results, with the wavelength as shown in the snapshot below.

What is the mass density μ of the string?

(a)   2.27 g/m
(b)   3.75 g/m
(c)   5.56 g/m
(d)   8.27 g/m
(e)   12.1 g/m

### QUESTION 20***

If the mass of the weight were quadrupled (i.e. increased to 17.2 kg), what would happen to the number of wavelengths in the standing wave?

(b)   It would double.
(c)   It would not change.
(d)   It would decrease by a factor of two.
(e)   It would decrease by a factor of four.

### QUESTION 21*

This and the following question relate to the same situation:

You are standing between two speakers. The speaker on the left is emitting a tone with frequency 306 Hz. The speaker on the right is emitting a tone with frequency 295 Hz. Irritated by the beats, you try to eliminate them by Doppler shifting the frequencies so you hear them as the same. The speed of sound is 343 m/s.

In which direction would you have to run to eliminate the beats?

(a)   left, towards the speaker with 306 Hz
(b)   right, towards the speaker with 295 Hz

### QUESTION 22**

How fast would you have to run?

(a)   6.3 m/s
(b)   10.2 m/s
(c)   14.8 m/s
(d)   19.4 m/s
(e)   26.6 m/s

### QUESTION 23*

A pipe organ with length 3.2 m is open at both ends. What is its fundamental frequency (corresponding to the longest possible wavelength)? The speed of sound is 343 m/s.

(a)   53.59 Hz
(b)   107.2 Hz
(c)   214.4 Hz

### QUESTION 24*

An aluminum plate at T = 20°C has a hole in the middle whose diameter is exactly 3 cm. What is the diameter of the hole if the plate is heated to 90°C? αAl = 2.25 × 10-7 K-1.

(a)   2.99990550 cm
(b)   2.99995275 cm
(c)   3 cm
(d)   3.00004725 cm
(e)   3.00009450 cm

### QUESTION 25***

A bar of copper (Cu) with length 2.635 m and a bar of aluminum (Al) with length 2.628 m are sitting at room temperature, T = 25°C. At what temperature will the two have the same length?

αCu = 1.60 × 10-7 K-1
αAl = 2.25 × 10-7 K-1.

(a)   6266 °C
(b)   21715 °C
(c)   21740 °C
(d)   41249 °C
(e)   41274 °C

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.