A river descends 15 m through rapids. The speed of the water is 3.2 m/s upon ent

Question

A river descends 15 m through rapids. The speed of the water is 3.2 m/s upon entering the rapids and 13 m/s upon leaving (a) What percentage of the gravitational energy of the water-Earth system is transferred to kinetic energy during the descent? (Hint: consider the descent of a specific mass of water, for example 10 kg.) (b) One of the "sinks" (types of energy that can't be turned back into mechanical energy) is thermal energy. Name another energy sink that drains away the potential energy the water-Earth system has at the top of the waterfall. (Hint: consider the water surface and watch the video at https: //www . youtube . com/watch?v=ynk4vJa-VaQ, also linked in Canvas Ch. 8 under the name "Water Droplet Physics.")

Explanation / Answer

by considering an aggregate of water of mass 1kg

loss of potential energy = mg?h = 1*15*9.8 J = 147 J

gain in kinetic energy =1/2 * m*[v^2-u^2]

gain in kE = 1/2*1*[(13^2) - (3.2^2)] J

gain in KE =79.38 Joules

so, 79.38/147 *100 = 54% energy is converted.

The remaining (100-54 = 46%) is dissipated through viscous forcesacting and causing heat in the water

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