**Second Examination
**

Physics 104

29 March 1977
#1. Skylab is a space station in free-fall orbit around earth.
Suppose an astronaut leaves Skylab and stands on its outer surface. Assume
the mass of Skylab is **4000 kg**, the mass of the space-suited astronaut is **100
kg**, and the distance between their centers-of-mass is **5.0 meters**.
Then the gravitational force of attraction (**in Newtons**) between the
astronaut and Skylab is most nearly equal to

**Answer:**

#2. A planet has a mass of **0.8** that of earth, and a radius of **0.5**
the radius of earth. The acceleration (**in m/sec**^{2}) due
to gravity at the planet's surface is most closely equal to

**Answer:**

#3. At a service station, in order to raise an automobile on a hydraulic
hoist, use is made of compressed air. The compressed air is introduced
into a tank (**4.0 inch diameter**) containing the hydraulic oil, as
indicated in the sketch. The oil, in turn, exerts a force on the hydraulic
piston (**8.0 inch diameter**) which raises the auto. If the maximum
weight of an automobile to be raised is **3.0 tons**, the air pressure (**in
lb/in**^{2}) that should be available is most closely equal to

**Answer:**

#4. Earth's mean distance from the sun is **1.49 ´
10**^{6} km, and that of Venus is **1.49 ´
10**^{6} km. The number of years required for Venus to
make one revolution around the sun is most closely equal Ito

**Answer:**

#5. A uniform spherical shell of mass** M**_{1} and outer
radius **R**_{1} has its center at a distance **D** from thee
center of a uniform solid sphere of mass **M**_{2} and radius **R**_{2}.
(See sketch.) A mass **m** lies within the spherical shell at a radius **r**
from its center and along the line joining the centers of the two spheres.
the total gravitational force acting on the mass **m** is equal to

**Answer:**

#6. The equation of a transverse wave traveling in a string is

**y =
(0.030 cm) ´ sin [0.20 px
/ cm - 200 pt / sec
] **

The amplitude (**in cm**) of the wave is most closely equal to

**Answer:**

#7. Given the wave of problem **#6**, the maximum transverse speed (**in
m/sec**) of a point fixed in the string is most closely equal to
**Answer:**

#8. A U-tube contains a liquid of unknown density **r**.
Water (density **r**_{W}) is poured into the right arm
to a depth **H**, and the liquid in the left arm rises to height ** h** above its level (at the water-liquid
interface) in the right arm, as shown in the sketch. The density of the liquid is equal to
**Answer:**

#9. At a certain point in a pipeline the water velocity is ** 2.0 m/sec** and the
gauge pressure is **1.5 ´10**^{4} Nt/m^{2}. At a
second point in the line ** one meter** lower than the first, if the cross-sectional
area at the second point is ** 0.5** that at the first, the gauge pressure (**in Nt/m**^{2}) is most
nearly equal to

**Answer:**

#10. A planet has mass** M** and radius **R**, and a space station circles
the planet at radius **r**. A projectile of mass **m** is to be
fired from the space station so that it will escape the planet's gravitational
influence completely. The **minimum velocity** of the projectile
(relative to the center of the planet) should be
**Answer:**

#11. A sphere containing men and equipment is raised from the bottom
of Lake Superior to a point just below the surface on an emergency cable.
The tension in the cable is determined to be **5000 lb**. If the sphere
has a diameter of **10.0 feet**, the minimum tension (**in lb**) that the
cable will have to support in order to raise the sphere completely out of the
water is most closely equal to
**Answer**

#12. An airplane has a wing area (each wing) of **100 ft**^{2}.
At a certain air speed, air flows over the upper wing surface at **160 ft/sec**,
and over the lower wing surface at **130 ft/sec**. Assume that the
plane travels at constant velocity, that lift effects associated with the
fuselage and tail assembly are small, and that the density of air is **2.54 ´10**^{-3}
slugs/ft^{3}. The weight (**in pounds**) of the airplane is
most closely equal to

**Answer:**

#13. Given the representation of a transverse wave in a spring pictured in the
sketch at **t = 0** and** x = 0**, respectively, an equation which
correctly represents the wave is

**Answer:**

#14. A spacecraft of mass** m** is in a free-fall, circular orbit of radius **R**
about a planet of mass **M**. the ** minimum additional energy** that the
spacecraft must be given in order to escape completely from the planet's
gravitational influence is equal to

**Answer**

#15. A container is filled with a hypothetical liquid having a density which
increases linearly with depth **y** below its surface: glass **r =
r**_{0} + k y, where ** r**_{0}
and ** k** are constants. If a side of the container has width W and depth **H**, the force due to the liquid on
the side is equal to
**Answer:**