; I. you are a design engineer in
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# I. you are a design engineer in

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You are a design engineer in a mattress factory. Your task is to organize a container of
miscellaneous springs based on their spring constant, but you don’t know the spring constants
of any of the springs. You have a stopwatch, a meterstick and a box of known masses.

a) Describe a method by which you can determine the spring constant of the springs.

b) Describe a second method that is different from the one you just described that you can
perform to independently validate your results in (a).

c) A 1.2 kg mass is hung from a spring and stretches it so that its equilibrium length
increases by ΔL=8 cm. If the mass-spring system oscillates at its natural frequency, how
long will it take for one period of oscillation?
II.     A standing wave on a 0.6 m string is described by the equation:

y=0.02 cos(5πx)cos(100πt)

where distances are measured in meters and time in seconds.

a) What are the amplitude and frequency of this standing wave?

b) Draw the standing wave pattern in the space below. Which harmonic is this?

n=

c) The string has a mass of .008 kg. Find the tension in the string.
III. A washing machine drum has a R=0.5 m radius and spins at and angular velocity of       ω
ω=+3 rev/s. A steady braking force of 100 N is applied at its edge and stops the
drum in 3.0 seconds.
R

a) Find the acceleration of the washing machine drum, and express your

b) Find the moment of inertia of the washing machine drum.

c) How much work is done by the braking force?
4. Two stars of masses M and 9M are separated by a distance D. Determine the distance
(measured from M) to a point at which the net gravitational force on a third mass would be
zero.

a) 0.75 D

b) 0.80 D

c) 0.50 D

d) 0.25 D

e) 0.20 D

spring
5. The spring scale shown in the diagram reads 200 N when a 25 kg object                             scale
is suspended in a fluid of density 6.0 x 102 kg/m3. Find the density of
the object (let g = 10 m/s2).

a)      1.2 x 103 kg/m3
fluid
b)      2.0 x 103 kg/m3

c)      12 x 103 kg/m3

d)      3.0 x 103 kg/m3

e)      6.0 x 103 kg/m3

6. A 0.8 m stick is suspended in static equilibrium as shown. A string
holding up the stick is hooked onto the wall. The left side of the stick
is held against the wall by the frictional force between it and the wall.
Assuming the stick is of uniform density, find the coefficient of
friction between the stick and the wall.                                       30°

a) 0.17
0.2 m
b) 0.50

c) 1.0

d) 0.42

e) 0.87
7. A 48.0 g block of ice at -15.0ºC is dropped into a calorimeter containing water at 15.0ºC.
When equilibrium is reached, the final temperature is 8.0ºC. How much water did the
calorimeter contain initially? The specific heat of ice is 2090 J/(kg K), the specific heat of
water is 2186 J/(kg K) and the latent heat of fusion of water is 335 × 103 J/kg.

a) 302 g

b) 405 g

c) 655 g

d) 634 g

e) 524 g

8. A balloon containing 2.0 m3 of hydrogen gas rises from a location at which the temperature is
22ºC and the pressure is 101 kPa to a location where the temperature is -39ºC and the
pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is
equal to the ambient pressure, what is the new volume of the balloon?

a)        2.0 m3

b)        4.0 m3

c)        6.0 m3

d)        8.0 m3

e)        10.0 m3

9. A gas expands from an initial volume of 0.040 m3 and an initial pressure of 210 kPa to a final
volume of 0.065 m3 while its temperature is kept constant. How much work is done by the
system?

a)       3.7 kJ

b)       4.1 kJ

c)       5.6 kJ

d)       7.9 kJ

e)       8.2 kJ
10. A Carnot engine has an efficiency of 83.0% and performs 4500 J of work every cycle. How
much energy is discharged to the lower temperature reservoir every cycle?

a) 922 J

b) 833 J

c) 744 J

d) 5422 J

e) 1577 J

11. An ideal gas undergoes the reversible process a→b→c→a shown below. Pa = Pc = 240 kPa,
Vb= Vc = 0.040 m3, Va = 0.015 m3, and Pb = 400 kPa. How much heat is gained by the system
in this process?

a) 1000 J

b) 1500 J

c) 2000 J

d) 2500 J

e) 3000 J

12. A very large open container of water drains at point c as shown below. If h=20 m then d is
closest to

a)    2m

b)    5m

c)    10 m

d)    20 m

e)    40 m
13. A glass tube that is closed at one end and open at the other is placed in front of a loud speaker
playing the sound made by a variable frequency audio oscillator. Standing waves are set up
in tube when the speaker emits a sound at 425 Hz and 1275 Hz. What is the length of the
tube (assume the speed of sound in air is 340 m/s)?

a)   10 cm

b)   20 cm

c)   30 cm

d) 40 cm

e)   50 cm

14. Sound emanating from a source is measured at 20 dB by an observer. To increase the sound
level to 40 dB, the intensity of the sound must be increased by:

a)       2

b)       4

c)       20

d)       100

e)       10,000

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