(b) If there is complete conversion of gravitational potential energy to kinetic energy, what is the speed of the water at the bottom of the fall?
(Note: This is actually an unrealistic assumption;
some of the energy in the fall will be converted into heat)
Mechanical energy is conserved
(EK + EP)top = (EK + EP)bottom
½ mv2top+ mgh = ½ mv2bot+ 0
v2bot = v2top + 2gh = (3.74 m/s)2 + 2(9.8 m/s2)(8.74 m) = 185.3
vbot = 14.4 m/s
Notice that the mass cancelled out. The result
be the same for a river of molten iron or a river of water. This is
aspect of what you already know-in the absence of friction all objects
fall the same distance in the same time.
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