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PS208 Practice Exam I ◊ Spring 2015
NAME:________________________________
The exam has two parts: a questions section with 4 multiple choice questions and a problems
section with 6 problems to solve. Please show your work for partial credit and clearly
indicate your answers. Anyone caught cheating on the exam will receive a failing grade.
Good luck! [gE=9.8 m/s2, 1 atm=1.013*105 Pa, 1 Pa=1 N/m2, G=6.67*10-11 N m2/kg2]
Questions (20 points): circle one or more choices, show your work for partial credit.
1. (5 points) An incompressible fluid flows through a pipe of varying radius (shown below in
cross-section). Compared to the fluid at point P, the fluid at point Q has
(a) greater pressure and greater volume flow rate.
(b) greater pressure and the same volume flow rate.
(c) the same pressure and greater volume flow rate.
(d) lower pressure and the same volume flow rate.
(e) none of the above
2. (5 points) The reason an astronaut in an earth satellite feels weightless is that
(a) this is a psychological effect associated with rapid motion.
(b) the astronaut is at a point in space where the effects of the moon's gravity and
the earth's gravity cancel.
(c) the astronaut's acceleration is zero.
(d) the astronaut is beyond the range of the earth's gravity.
(e) the astronaut is falling.
3. (5 points) In simple harmonic motion, the speed is greatest at that point in the cycle
when
(a) the kinetic energy is a minimum.
(b) the magnitude of the acceleration is a minimum.
(c) the potential energy is a maximum.
(d) the displacement is a maximum.
(e) the magnitude of the acceleration is a maximum.
4. (5 points) Because the earth's orbit is slightly elliptical, the earth actually gets closer to
the sun during part of the year. When the earth is closer to the sun its orbital speed is
(a) greater than when the earth is farthest away from the sun.
(b) the same as when the earth is farthest away from the sun.
(c) less than when the earth is farthest away from the sun.
Problems:
1. (10 points) You are stranded on a certain spherical asteroid with a diameter of 11.2 km
and a mass of 2.13*1015 kg. You want to play a game of baseball by yourself with a 0.76 kg
ball. What initial speed do you need to give the ball to put it in a circular orbit just above
the surface?
v0=_____________m/s
Problems 2 & 3: The horizontal pipe shown in the figure has a cross sectional area of 40.0
cm2 at the wider portions and 10.0 cm2 at the constriction. Water is flowing in the pipe, and
the discharge rate from the pipe is 8.25*10-3 m3/s. [!w=1.0*103 kg/m3]
2. (10 points) What is the flow speed in the wide (1) and narrow (2) portions?
v1=____________m/s
v2=____________m/s
3. (10 points) What is the pressure difference between these portions?
P1-P2=______________ Pa
4. (20 points) A uniform sphere with mass 25.0 kg is held with its center at the origin, and
a second uniform sphere of mass 50.0 kg is held with its center at the point x=0 m, y=-3.00
m. What is the magnitude and direction of the net gravitational force due to these objects
on a third uniform sphere with mass 2.35 kg placed at the point x=4.00 m, y=0 m?
Fnet=_______________N
Direction=______________
5. (10 points) The motion of the piston of an automobile engine is approximately simple
harmonic motion, as shown in the figure. If the stroke of an engine (twice the amplitude) is
0.100 m and the engine runs at 4300 rpm (rev/min), compute the maximum speed of the
piston.
vmax=________________m/s
6. (20 points) You want to float a balloon on Mars where the atmospheric density is 0.0154
kg/m3. The balloons are constructed out of a thin but tough plastic with density such that
each square meter is 5.00 grams. They are inflated with a very light gas whose mass we can
ignore. What radius and mass of these balloons is needed to just hover over the surface?
R=______________m
m=_________________kg