7-49(b).A river is flowing with a speed of 3.74 m/s just upstream from a waterfall of vertical height 8.74 m. During each second 7.12X104 kg of water pass over the fall.
(a) [We will ignore this part]

(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 would be the same for a river of molten iron or a river of water. This is another 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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