1.4 Practice Problem Transcribed Image Text: Problems 27 1.2. Calculate the altitude at which an artificial satellite orbiting in the equa- torial plane can be

1.4 Practice Problem Transcribed Image Text: Problems
27
1.2. Calculate the altitude at which an artificial satellite orbiting in the equa-
torial plane can be a synchronous satellite (i.e., can remain above the same
spot on the surface of Earth).
1.3. An artificial satellite is placed in a natural synchronous orbit above the
equator and is attached to Earth below by a wire. A second satellite is
attached to the first by a wire of the same length and is placed in orbit
directly above the first at the same angular velocity. Assuming that the wires
have zero mass, calculate the tension in the wires per unit mass of satel-
lite. Could this tension be used to lift objects into orbit with no additional
expenditure of energy?
1.4. A train is running smoothly along a curved track at the rate of 50 ms-1.
A passenger standing on a set of scales observes that his weight is 10%
greater than when the train is at rest. The track is banked so that the force
acting on the passenger is normal to the floor of the train. What is the radius
of curvature of the track?
1.5. If a baseball player throws a ball a horizontal distance of 100 m at 30°
latitude in 4 s, by how much is the ball deflected laterally as a result of the
rotation of Earth?
1.6. Two balls 4 cm in diameter are placed 100 m apart on a frictionless hori-
zontal plane at 43°N. If the balls are impulsively propelled directly at each
other with equal speeds, at what speed must they travel so that they just
miss each other?
1.7. A locomotive of mass 2 × 105 kg travels 50 ms-l along a straight horizontal
track at 43°N. What lateral force
exerted on the rails? Compare the mag-
nitudes of the upward reaction force exerted by the rails for cases where
the locomotive is traveling eastward and westward, respectively.
1.8. Find the horizontal displacement of a body dropped from a fixed platform
at a height h at the equator, neglecting the effects of air resistance. What is
the numerical value of the displacement for h = 5 km?
1.9. A bullet is fired directly upward with initial speed wo at latitude o. Neglect-
ing air resistance, by what distance will it be displaced horizontally when
it returns to the ground? (Neglect 22u cos o compared to g in the vertical
momentum equation.)
1.10. A block of mass M = 1 kg is suspended from the end of a weightless string-
The other end of the string is passed through a small hole in a horizontal
platform and a ball of mass m = 10 kg is attached. At what angular veloc-

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