a 245-kg boulder is dropped into a mine shaft thats is 3.0x10^3 m deep. During t

Question

a 245-kg boulder is dropped into a mine shaft thats is 3.0x10^3 m deep. During the boulder's fall, the system consisting of the earth and boulder loses a certain amount of gravitational potential energy. it would take an equal amount of energy to "free" the boulkder from the shaft by raising it back up to the top, so this can be considered the system's binding energy (a) determine the binding energy in joules of the system and (b) how much mass does the system lose when the boulder falls to the bottom of the shaft?

Explanation / Answer

The mass of the boulder m = 245 kg The depth of the mine shaft h = 3.0*10^3 m The binding energy is provided by potential energy therefore the binding energy                   E = mgh                      = (245 kg)(9.8 m/s^2) (3*10^3m)                      = 7.2*10^6 J (b) From mass energy relation              E = mc^2 therefore the mass lost              m = E/c^2                     = (7.2*10^6J)/(3*10^8 m/s)^2                     = 8*10^-11 kg                  

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