Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 8 - Potential Energy and Conservation of Energy - Problems: 123

Answer

54% of the energy

Work Step by Step

The river descends 15m and has an initial speed of 3.2 m/s. It leaves with 13 m/s. Considering 10kg of water (as in the hint), we can find the initial potential energy using U = mgd = (10kg)(9.8)(15m) = 1470 Joules. Using conservation of mechanical energy, we know that the change in kinetic energy must come due to a decrease in kinetic energy. We can find the change in kinetic energy by $\Delta KE = (1/2)m(v_{f}^2-v_{i}^2) $ = 793.8 Joules. The percentage of the original is therefore (793.8J/1470J) = 0.54 or 54%
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