A 283-kg boulder is dropped into a mine shaft that is 4.5 A 283-kg boulder is dr

Question

A 283-kg boulder is dropped into a mine shaft that is 4.5

A 283-kg boulder is dropped into a mine shaft that is 4.5 times 103 m deep. During the boulder's fall, the system consisting of the Earth and the boulder loses a certain amount of gravitational potential energy. It would take an equal amount of energy to "free" the boulder from the shaft by raising it back to the top, so this can be considered the system's "binding energy." (a)Determine the binding energy (in Joules) of the Earth-boulder system. (b) How much mass does the Earth-boulder system lose when the boulder falls to the bottom of the shaft?

Explanation / Answer

the binding energy is

U = (GMm/r)

where G = 6.67 x 10^-11 Nm^2/kg^2,M = 5.98 x 10^24 kg,m = 283 kg and r = 4.5 x 10^3 m

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