AJM:4/4/02 Score /100
Physics 132 Midterm Winter 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. 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
give partial credit, but only if I can figure out what you are doing, so be as clear as possible.
1. [10 pts] Fill out a simple table showing both the SI units and the dimensions of the indicated quantities:
i) pressure, p ii) the force constant of a spring, k iii) the universal gravitation constant, G
2. [10 pts] A periodic wave with a frequency of 30 Hz and a wavelength of 40 cm travels along a string that is 8.0 m long
and has a total mass of 200 g. What is the tension in the string?
3. [10 pts] A mass is attached to a spring as shown at right. It is then pulled to the
right some distance and released at rest. Just after being released its acceleration is
60 m/s2. As it passes the equilibrium position it has a speed of 5.0 m/s. The total
energy of oscillation is 16 J. What is the angular frequency of oscillation? (Big hint: How are the indicated
acceleration and speed related to the angular frequency and amplitude?)
EXTRA CREDIT [5 pts] Suppose that I use a mass that is twice as large, but that I pull it the same distance away
before releasing it in the same way. Now what is the
i) initial acceleration ii) total energy of oscillation iii) speed as it passes the equilibrium position
4. Io is a moon of Jupiter that is approximately the size and mass of Earth’s moon and whose nearly circular orbit also has
approximately the same radius as that of Earth’s moon. To be specific, Io has a mass of 8.9 x 1022 kg, an orbital radius
of 4.2 x 105 km and an orbital period of 1.77 days.
a) [4 pts] Why does this information tell us that the mass of Jupiter must be larger than that of the Earth? (Big hint:
Compare the orbital periods and radii of the two bodies!)
b) [4 pts] What is the orbital speed of Io? [Please don't make this complicated. It isn’t!]
c) [12 pts] Starting with Newton’s second law (write it down!), applying it to Io, using Newton’s law of gravitation,
and assuming that Io's orbit is circular, obtain an equation and use it to find the mass of Jupiter.
5. A large, open air storage tank is filled with 20 m3 of water. A pipe leads out of
the bottom as shown and then turns upward . At its open air outlet, the pipe has
a radius of 3.0 cm.
a) [10 pts] What is the speed of the water as it emerges from the pipe?
b) [5 pts] Approximately how long will it take to empty the tank? [Hint:
Assume that the speed of the outflowing water doesn’t change much.]
EXTRA CREDIT [5 pts] With the tank full, how high does the water shoot
above the end of the pipe AND how would this answer change if you lowered the
end of the pipe by 1.0 m?
[OVER for MORE]
V = 20 m
3
r = 3.0 cm
v
h = 5.0 m
d = 2.0 m
