AJM:4/11/05 Score /100
Physics 132 Midterm Spring 2002
Name
!
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read
each problem carefully. The credit you receive on each problem will depend at least as much on how you get your answer as
on what answer you get. There is no need to be as “wordy” as I ask you to be on homework, but you must show your work
or give at least a brief explanation for every answer. I give no credit for unsupported answers. I give partial credit for
partially correct solutions, but only when I can figure out what you are doing, so be as clear as possible. Make certain that
all numerical answers are given with a reasonable number of significant digits (when in doubt, three is usually a good
compromise) and that you have included appropriate and simplified units. Check your answers for physical reasonableness
whenever possible; I do deduct points for ridiculous answers that go uncommented upon.
1. [10 pts] Complete a table with the SI units and the dimensions of
i) linear mass density,
µ
ii) angular frequency,
ω
iii) power, P
2. [10 pts] Find the mass of the Earth from the known values of g, G (
6.67×10 −11 N⋅m2/kg 2
), and
Rearth
(
6.37×10 6 m
)
3. Two wave pulses travel toward each other as shown at right in
a medium that has a wave speed of 50 m/s.
a) [5 pts] About how long a time will it be before the
“peaks” of the two pulses coincide spatially.
b) [5 pts] Sketch the waveform at the time that the peaks coincide. [Be careful; this isn’t hard, but it also isn't trivial.]
4. A particle in simple harmonic motion reaches its maximum positive velocity of 5.0!m/s at a time that is
150!milliseconds before it reaches its maximum negative distance from the equilibrium position.
a)![5 pts] What is the angular frequency of oscillation? [Hint: You might want to sketch a graph of x versus t first.]
b) [5 pts] What is the oscillation amplitude?
5. A dam is built to keep the very salty water of the Salton Sea (density
ρ
s = 1.060 g/cm3)
from intruding into a pond that is fed by freshwater (density
ρ
f = 1.000 g/cm3) streams. In
order to prevent the fresh water pond from filling and overflowing the dam, a small pipe is
installed 8.0 m below the sea surface that is intended to allow fresh water to flow out of the
pond.
a) [6 pts] Explain why, in fact, salt water will flow into the pond if the surface levels on
each side of the dam are the same—unlike what is shown in the drawing. [Hint:
Consider the pressure on either end of the pipe in that situation.]
b) [14 pts] Now suppose that there is no flow either way through the pipe. Find the
difference in the surface levels on either side of the dam.
6. A sinusoidal wave with a frequency of 100 Hz and a wavelength of 40 cm travels along the thick part of a taut string
made of two 5.0 m lengths of string joined in the middle. Both parts of the string are made of the same material and are
under the same tension of 80 N, but the thin part has one half the diameter of the thick part.
a) [5 pts] Explain briefly, but precisely why the thin part has one quarter the linear mass density of the thick part.
b) [5 pts] Using the result of part a, how does the speed of the wave in the thinner string compare to that in the thicker
string? (That is, simply find
vthin /vthick
.)
c) [5 pts] How long a time does it take a wave to travel the full 10 m length of this string?
d) [5 pts] What are the frequency and wavelength of the wave in the thinner part?
EXTRA CREDIT [5 pts] What is the total mass of the composite string?
7. Consider a system of three identical stars—each with mass M—two of which orbit about a
motionless third star along the same circular path of radius R as shown at right.
a) [5 pts] Explain briefly but completely how the central star is able to remain
motionless while the other two move around the circular path.
b) [5 pts] Find the magnitude of the net force on either of the two orbiting stars (in
terms, of course, of the givens—M and R.)
c) [10 pts] Therefore, find the orbital period of either orbiting star (in terms of M and R.
EXTRA CREDIT [5 pts] Suppose that M = the mass of the sun =
2×1030 kg
and R = the distance from the Earth to
the Sun =
1.5 ×1011 m
. How would you expect the orbital period of this star system to compare to the orbital period of
the Earth about the Sun? Specifically, should it be longer, shorter, or the same?
2 m
3 m
4 m
5 m
6 m
7 m
sea
fresh
8.0 m