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:

a) 0.25     b) 980    c) 1.1 ´ 10-6     d) zero     e) 16000    

#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/sec2) due to gravity at the planet's surface is  most closely equal to
Answer:

a) 31       b) 4         c) 0.5        d) 0.4     e) 1.3

#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/in2) that should be available is most closely equal to
Answer:

a) 950        b) 120          c) 60           d) 480         e) 240     

#4.  Earth's mean distance from the sun is  1.49 ´ 106 km, and that of Venus is 1.49 ´ 106 km.  The number of years required for Venus to make one revolution around the sun is most closely equal Ito


Answer:
a) 0.62      b) 1.4      c) 1.6      d) 0.72      e) 4.6

#5.  A uniform spherical shell of mass M1 and outer radius R1 has its center at a distance D from thee center of a uniform solid sphere of mass M2 and radius R2. (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:
a) G m[M1/R1+M2/R2   b) GM2m/(D-r)2-GM1m/r2  c)GM1m/r d) GM2m/(D-r) e) zero

#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:
a) 0.628    b) 0.030  c) 10  d) 1000   e) 19

#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:

a) 10 b) 0.628 c)  0.030 d) 19 e)  1000

#8. A U-tube contains a liquid of unknown density r.  Water (density rW) 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:
a) rW H/h    b) rW (H-h)/H      c) rW g h     d) rWg (H+h)    e) rW h/(H+h)

#9. At a certain point in a pipeline the water velocity is 2.0 m/sec and the gauge pressure is 1.5 ´104 Nt/m2. 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/m2) is most nearly equal to
Answer:
a) 9800      b) 6000      c) 15000     d) 11200      e) 18800

#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:

a) GMm/R2    b) Ö(2GMm/R)   c) Ö(GM(r-R))   d) Ö(2GM/R)   e) Ö(Gmr) / R

#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

a) 5000    b) 9900    c) 32700   d) 10000  e) 62400

#12. An airplane has a wing area (each wing) of 100 ft2.  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/ft3.  The weight (in pounds) of the airplane is most closely equal to
Answer:
a) 354   b) 2200  c) 5000    d) 230    e) 70400

#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:
a)  y = (5 cm) ´  sin [ px / (6 cm) - 200 pt / s] 
b) y =   (5 cm) ´  sin [x /(12 cm) - t /(0.01 sec)] 
c) y =   (12 cm) ´  sin [5x / cm - 0.01 t / sec] 
d) y =   (5 cm) ´  sin [0.12 px / cm - 200 t / sec] 
e) y =   (5 cm) ´  sin [0.20 px /(12 cm) + t /(0.01 sec)] 

#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
a) GMm/R  b) GMm/(2R)  c) zero  d) Ö(2GM/R   e) Ö(GM/R2)

#15. A container is filled with a hypothetical liquid having a density which increases linearly with depth y below its surface: glass r = r0 + k y, where r0 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:
a) WH2 r0g
b) WH2 (r0 + kH) / 6
c) WH2 g( 3 r0 + 2kH) / 6
d) WH2 g/2
e) WgH (r0 + kH)/3