### Spring 2006 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 107; the average score was 87.9; the median score was 91. 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 and the following two questions relate to the same situation:

A block of mass 6.0 kg resting on a horizontal frictionless surface is attached to a spring with force constant k = 210 N/m. A force of F is applied to the block in the x-direction, thereby compressing the spring from its equilibrium length (see picture) by 0.1m.

What is the magnitude of force F?

(a)   8 N
(b)   10 N
(c)   17 N
(d)   18 N
(e)   21 N

### QUESTION 2*

The force is removed and the block starts to oscillate. What is the period of this oscillation?

(a)   0.01 sec
(b)   0.3 sec
(c)   1.1 sec
(d)   1.4 sec
(e)   9.3 sec

### QUESTION 3*

If we repeated the experiment but now with a force that is double in size, i.e. F replaced by 2F, how does the oscillation frequency of the block change?

(a)   It becomes twice as large.
(b)   It becomes four times as large.
(c)   It does not change.

### QUESTION 4**

A police car is sounding its siren. As it approaches a stationary person, she hears a tone of 480 Hz. As the police car goes away, she hears a tone of 430 Hz. How fast is the police car moving? (The speed of sound in air is 330 m/s.)

(a)   0.5 m/s
(b)   0.7 m/s
(c)   11 m/s
(d)   13 m/s
(e)   18 m/s

### QUESTION 5*

This and the following question relate to the same situation:

An archer pulls the bowstring back a distance of 0.2 m before releasing the arrow. Consider that the bow and string act like a spring with a spring constant of 230 N/m. The arrow has a mass of 0.03 kg.

What is the magnitude of the spring potential energy of the drawn bow?

(a)   2.3 J
(b)   4.6 J
(c)   6.2 J
(d)   7.4 J
(e)   9.2 J

### QUESTION 6*

What is speed of the arrow when it leaves the bow?

(a)   8.5 m/s
(b)   10.2 m/s
(c)   17.5 m/s
(d)   19.3 m/s
(e)   23.4 m/s

### QUESTION 7*

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

A simple pendulum is constructed of a 0.4-kg mass (the bob) hanging on a massless string. How long is the string if the pendulum oscillates with a period of 2 s?

(a)   26 cm
(b)   42 cm
(c)   58 cm
(d)   73 cm
(e)   99 cm

### QUESTION 8*

If 'the bob' of the pendulum is displaced by 3 cm in the horizontal direction (the x-direction) and let go at time t = 0, which of the following equations will describe the time dependence of the distance of the mass from its equilibrium position? (The angular frequency of the oscillation is denoted by ω).

(a)   x(t) = 3 sin(ωt) cm
(b)   x(t) = 3 cos(ωt) cm
(c)   x(t) = -3 sin(ωt) cm

### QUESTION 9**

Suppose that the same pendulum is in an elevator that is accelerating downward. It's period will be

(a)   more than 2 s.
(b)   less than 2 s.
(c)   2 s.

### QUESTION 10*

A balloon is filled at atmospheric pressure (1.01 × 105 Pa), and room temperature (293K) with an ideal gas to a volume of 0.07 m3. How many molecules of gas are in the balloon?

(a)   0.28 × 1024
(b)   1.17 × 1024
(c)   1.75 × 1024

### QUESTION 11*

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

The wavelength of the fundamental mode of the string in a newly designed stringed instrument is 1.8 m. What is the length of the string? (Note that the string is fixed at both ends.)

(a)   0.45 m
(b)   0.9 m
(c)   1.8 m

### QUESTION 12*

The string has a mass density of 9 × 10-4 kg/m and it is vibrating in the fundamental mode at a frequency of 350 Hz. What is the tension in the string?

(a)   95 N
(b)   146 N
(c)   212 N
(d)   357 N
(e)   428 N

### QUESTION 13**

Suppose the mass of the string in the above problem is M0. What is the mass of a new string (in terms of M0 ), if the fundamental frequency of the string is doubled compared to the previous value, but the length and tension in the string are the same as before?

(a)   4 M0
(b)   M0
(c)   M0 / 4

### QUESTION 14*

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

A plastic cube (ρ = 780 kg/m3, V = 0.71 m3) is suspended by a string such that half the volume is submersed in water (ρ = 1000 kg/m3) as shown in the figure.

What is the tension T in the string?

(a)   372 N
(b)   428 N
(c)   931 N
(d)   1950 N
(e)   2380 N

### QUESTION 15*

The string is cut. What fraction of the volume is now below the surface of the water?

(a)   22%
(b)   78%
(c)   93%

### QUESTION 16*

How much weight could be placed on top of the block, so that the block just floats, but is submerged under the surface of the water?

(a)   98 kg
(b)   123 kg
(c)   156 kg

### QUESTION 17**

This and the following question relate to the same situation:

An open-tube manometer is shown to the right. Fluid A is water (ρ = 1000 kg/m3). Fluid B is oil (ρ = 910 kg/m3).

Which pairs of points in the figure have equal pressure?.

(a)   P1 = P5
(b)   P2 = P5
(c)   P3 = P4
(d)   P1 = P5 and P3 = P4
(e)   P2 = P5 and P3 = P4

### QUESTION 18**

Calculate h, the difference in height between the top of the fluid on the left side and the right side.

(a)   0.01 m
(b)   0.03 m
(c)   0.05 m
(d)   0.15 m
(e)   0.30 m

### QUESTION 19**

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

Water (density = 1000 kg/m3) flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference between the two tubes is 7,500 Pa. Which tube has the higher pressure?

(a)   the one with the larger diameter
(b)   the one with the smaller diameter

### QUESTION 20*

Suppose the flow speed is V in the 2.8 cm diameter tube. What is the flow speed in the 1.6 cm diameter tube?

(a)   1.75 V
(b)   3.06 V
(c)   5.33 V

### QUESTION 21**

What is the flow speed V in the 2.8 cm diameter tube?

(a)   0.15 m/s
(b)   1.3 m/s
(c)   2.6 m/s
(d)   5.2 m/s
(e)   11.0 m/s

### QUESTION 22*

This and the following question relate to the same situation:

The small piston of a hydraulic lift has a cross sectional area of 3 cm2 . You need to lift a 15,000 N weight by applying a force of only 200 N.

What is the area of the large piston, assuming both pistons are at the same height, as shown in the drawing?.

(a)   75 cm2
(b)   125 cm2
(c)   225 cm2

### QUESTION 23**

If you push the small piston down a distance of 25 cm. How far up does the weight move?

(a)   0.3 cm
(b)   8.2 cm
(c)   25 cm

### QUESTION 24*

Two metal rods, one made from aluminum (α = 22.5 × 10-6/K) and the other from steel (α = 12.0 × 10-6/K), have the same length (Lo = 5 m) at room temperature (To = 20°C). What is the difference between the length of the aluminum rod and the steel rod when they are both 58°C?

(a)   Laluminum - Lsteel = -3 mm
(b)   Laluminum - Lsteel = -2 mm
(c)   Laluminum - Lsteel = 0 mm
(d)   Laluminum - Lsteel = +2 mm
(e)   Laluminum - Lsteel = +3 mm

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.