8. Centripetal Forces & Gravitation

Suppose a 1,800-kg car passes over a bump in a roadway that follows the arc of a circle of radius 20m. What
force does the road exert on the car as the car moves over the top of the bump if the car moves at a constant 9 m/s?

(II) At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5–45) do not fall out? Assume a radius of curvature of 7.6 m.

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(II) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 5–47. The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect nearly equal to gravity at the surface of the Earth, 0.90 g, is to be felt by astronauts walking inside? Which part of the tube do they walk on?

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(II) A pilot performs an evasive maneuver by diving vertically at a constant 310 m/s. If he can withstand an acceleration of 9.0 g’s without blacking out, at what altitude must he begin to pull his plane out of the dive (moving in a vertical circular path) to avoid crashing into the sea?