AJM:1/1/02 Score /100
Physics 132 Exam #1 Winter 2001
Name
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read
each problem carefully. Show your work and/or give brief explanations for all answers. (But there is no need to be as
“wordy” or formal as on the homework.) Make sure that all numerical answers are given with a reasonable number of sig
figs and that you have included appropriate units. Check your answers for physical reasonableness whenever possible. I do
give partial credit, but only if I can figure out what you are doing, so be as clear as possible.
1. A 2.0 kg object attached to a spring oscillates freely with a period of 3.0 s and a total energy of 10.0 J.
a) [10 pts] What is the spring constant?
b) [10 pts] What is the amplitude of the oscillation?
2. Astronomers announce the discovery of an amazing system of three identical stars of
mass m forming and maintaining an equilateral triangle of side d as they orbit about
their common center of mass along a common circular path as shown at right.
a) [4 pts] Explain briefly and clearly why the net gravitational force on each star is
directed toward the center of mass (the center of the common circular orbit.)
b) [10 pts] Find the magnitude of the net force acting on each star in terms of G, m,
and d. (Vector addition!)
c) [4 pts] Find the radius of the circular orbit in terms of d. (Geometry!)
d) [8 pts] Find the orbital period—i.e., how long a time it takes for each star to complete one orbit—in terms of G,
m, and d. (You will need to apply Newton’s second law to one of the stars and express its acceleration in terms of
the orbital radius and the period of the orbit.)
e) [4 pts] The astronomers can only measure the distance between the stars and the orbital period. Explain how that
information allows them to determine the mass of the stars.
3. A dam is built to keep salty sea water (density ρs = 1.040 g/cm3) from intruding into a
lagoon that is fed by freshwater (density ρf = 1.000 g/cm3) streams. In order to prevent
the fresh water lagoon from filling and overflowing the dam, a pipe is installed 20 m
below the sea surface that is intended to allow fresh water to flow into the sea.
a) [8 pts] Explain why, in fact, salt water will flow into the lagoon if the surface levels
on each side of the dam are the same. (Unlike what is shown in the drawing!)
b) [12 pts] Now suppose that there is no flow either way through the pipe. Find the
difference in the levels of the two surfaces.
4. [6 pts] Water flows through a pipe as shown at right. Rank the pressures at the indicated
positions from highest to lowest and explain the reasons for your ranking order in terms of
physical principles.
5. [6 pts] A hot air balloon uses burners placed below an opening in the balloon envelope to heat
the air inside the balloon. Briefly and clearly explain the purpose of the hot air in terms of Archimedes’s principle.
6. [6 pts] Consider a planet that has the same average density as Earth, but half its radius. What would the gravitational
field strength (also known as “the acceleration due to gravity”) be near its surface? (Hint: Think proportionally! How
does the mass of the planet compare to that of Earth?)
7. Two transverse wave pulses on a rope travel toward each other as
shown at right.
a) [6 pts] Sketch the shape of the rope at the specific time when
the peak of one pulse meets the peak of the other.
b) [6 pts] Sketch a plot of the displacement of point A on the rope as a function of time. (Think about what that
specific point does as the two pulses move along and travel past it.)
CM
d
d d
m m
m
sea fresh
20 m
A B C
A