### Fall 2006 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 102. The exam period was 90 minutes; the average score was 79.0; the median score was 83. 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 three questions relate to the same situation:

A 3 kg pendulum is placed on an elevator next to a 3 kg mass hung vertically by a spring with spring constant 200 N/m. When the elevator is at rest, the pendulum and the mass on the spring oscillate with the same period.

What is the length of the pendulum?

(a)   9 cm
(b)   15 cm
(c)   23 cm
(d)   27 cm
(e)   32 cm

### QUESTION 2*

The unstretched length of the spring without the mass is 0.4 meters. What is the equilibrium length of the spring with the 3 kg mass attached when the elevator is at rest?

(a)   0.55 m
(b)   0.69 m
(c)   0.83 m

### QUESTION 3**

The mass on the spring is observed to be moving 3 m/s when the spring is stretched 0.2 meters from its equilibrium position. What is the maximum speed of the mass as it oscillates up and down.

(a)   3.4 m/s
(b)   4.2 m/s
(c)   5.1 m/s

### QUESTION 4**

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

Compare the period of the pendulum Tpendulum to the period of the mass on the spring Tmasss on spring when the elevator is accelerating up.

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

### QUESTION 5**

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

At an air show, a jet flies past you. The sound from the engine is 90 dB when it is 700 meters away.

How far away must the engine be, so that the intensity of the sound is reduced by a factor of 8?

(a)   8 × 700 m
(b)   4 × 700 m
(c)   sqrt(8) × 700 m

### QUESTION 6**

How loud is the jet when the intensity of the sound has been reduced by a factor of 8?

(a)   89 dB
(b)   81 dB
(c)   11 dB

### QUESTION 7**

As the jet is flying toward you at 180 m/s, you hear the frequency of the sound from the jet as 420 Hz. What frequency will you hear as the jet flies away from you at 180 m/s? (Note that the speed of sound is v = 340 m/s).

(a)   129 Hz
(b)   240 Hz
(c)   310 Hz
(d)   380 Hz
(e)   420 Hz

### QUESTION 8*

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

A piano string is fixed at both ends 0.78 meters apart and has a mass of 0.0028 kg.

What is the fundamental wavelength of this string?

(a)   0.39 m
(b)   0.78 m
(c)   1.56 m

### QUESTION 9*

What is the tension in the string, if the fundamental frequency for the string is 450 Hz?

(a)   550 N
(b)   990 N
(c)   1220 N
(d)   1550 N
(e)   1770 N

### QUESTION 10*

What is the wavelength of the sound wave produced by this string vibrating at 450 Hz? (v = 340 m/s)

(a)   0.75 m
(b)   1.56 m
(c)   2.41 m

### QUESTION 11**

A balloon is filled with 0.8 liters of air, at 20°C and sealed. The balloon is then heated so the air inside is 60°C. What is the new volume of the balloon? (You may assume the pressure in the balloon remains constant as the balloon stretched).

(a)   0.91 liters
(b)   1.4 liters
(c)   2.4 liters

### QUESTION 12**

One liter of water at 20°C (β = 207 × 10-6 /K) is placed in a metal (α = 16 × 10-6 /K) cube, whose each side is length 0.1 m so that it can hold exactly one liter. The water and cube are heated to 80°C. How much water spills out of the pan?

(a)   5.03 × 10-4 liters
(b)   9.54 × 10-3 liters
(c)   14.1 × 10-3 liters

### QUESTION 13**

Fluids A and B are poured into a U-shaped pipe, shown below. Fluid A is water
(ρ = 1000 kg/m3), which rises 0.4 m above the bottom of the left pipe, and 0.2 m above the bottom of the right pipe. Fluid B in the right pipe rises 0.5 m above the level of water.

What is the density of Fluid B?

(a)   400 kg/m3
(b)   600 kg/m3
(c)   1000 kg/m3
(d)   1250 kg/m3
(e)   2500 kg/m3

### QUESTION 14**

A house has a 9 m wide and 11 m long flat roof. What is the lift on this roof when a 20 m/s wind blows over it? The density of air is 1.29 kg/m3.

(a)   19.8 × 103 N
(b)   21.5 × 103 N
(c)   23.0 × 103 N
(d)   25.5 × 103 N
(e)   27.0 × 103 N

### QUESTION 15*

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

A string holds an oak cube (ρO = 600 kg/m3, volume V = 0.8 m3) to the bottom of a pool. The pool is filled with water (ρW = 1000 kg/m3). The tension in the string is T = 2500 N.

What is the volume of the part of the cube under water, V1?

(a)   V1 = 0.60
(b)   V1 = 0.64
(c)   V1 = 0.70
(d)   V1 = 0.74
(e)   V1 = 0.80

### QUESTION 16*

We cut the string. The volume of the part of the cube under water is now V2. What fraction of the volume of the cube is under water now?

(a)   V2 / V = 0.4
(b)   V2 / V = 0.6
(c)   V2 / V = 0.8

### QUESTION 17*

We put a weight on the top of the oak cube so the cube gets immersed as deep as it was before the string was cut. What is the additional mass M?

(a)   M = 155 kg
(b)   M = 205 kg
(c)   M = 255 kg

### QUESTION 18*

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

A hydraulic lift is filled with oil (ρ = 700 kg/m3). The cross section area of the large piston in the cylinder on the right is A2 = 180 cm2. The area of the small piston in the cylinder on the left is A1 = 0.4 cm2.

What force F1 do we need to apply to the small piston to lift a 20000 N weight so the bottom of both pistons is at the same height?

(a)   F1 = 4.44 N
(b)   F1 = 44.44 N
(c)   F1 = 444.44 N

### QUESTION 19*

How much does the load go up when the small piston is pushed down 25 cm?

(a)   0.055 cm
(b)   0.075 cm
(c)   103.0 cm

### QUESTION 20***

Assume now that we apply force F1 again to the small piston, so the two pistons are at the same level. How much more force, ΔF, has to be applied to the small piston to hold the load 0.1 m above the level of the small piston?

(a)   0.027 N
(b)   0.225 N
(c)   314.0 N

### QUESTION 21*

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

Water flows through a pipe with the cross section area A1. The pipe is connected to a wider pipe with the cross section area A2 = 20 cm2. The velocity of water in the narrow pipe is v1 = 3.00 m/s, and in the wider pipe it is v2 = 0.6 m/s. The density of water is 1000 kg/m3.

Define P1 = the water pressure in the narrow pipe, and P2 = the water pressure in the wider pipe. Which one of these statements is correct?

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

### QUESTION 22*

What is the cross section of the narrow pipe, A1?

(a)   A1 = 3.00 cm2
(b)   A1 = 3.75 cm2
(c)   A1 = 4.00 cm2

### QUESTION 23*

What is the absolute value of the water pressure difference, |ΔP| = |P1 -P2| between the wide and narrow parts of the pipe?

(a)   |ΔP| = 0
(b)   |ΔP| = 173 Pa
(c)   |ΔP| = 208 Pa
(d)   |ΔP| = 503 Pa
(e)   |ΔP| = 4320 Pa

### QUESTION 24*

This and the following question relate to the same situation:

The submersible Alvin, which has been in service since 1964, has been used for biological research as well as for dives to the Titanic. It can dive down to the depth of about 4500 m.

On an average dive, Alvin dives to the depth of 2000 meters. What is the pressure at this depth, P2000? The density of the seawater, ρseawater = 1030 kg/m3.

(a)   P2000 = 1.8 106 Pa
(b)   P2000 = 1.0 107 Pa
(c)   P2000 = 2.0 107 Pa
(d)   P2000 = 3.5 107 Pa
(e)   P2000 = 4.0 107 Pa

### QUESTION 25*

At another depth, the water pressure around Alvin is 4.9 × 107 Pa. Alvin's titanium pressure hull has a round flat window with a 10 cm radius. What is the total force F acting on the window at this depth?

(a)   0.5 × 105 N
(b)   1.0 × 105 N
(c)   7.5 × 105 N
(d)   1.5 × 106 N
(e)   2.0 × 107 N

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.