Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 6 - Work and Energy - Problems - Page 171: 82


$\overline P=1.69\times10^4W$

Work Step by Step

According to the work-energy theorem, $$W=\frac{1}{2}m(v_f^2-v_0^2)$$ We have $m=184kg, v_0=0,$ and $ v_f=26m/s$, so the amount of work which must be done by the winch is $$W=62192J$$ To find the power the winch must supply, we also need to find the amount of time to accelerate the glider, which can be found with the equations of kinematics: $$s=\Big(\frac{v+v_0}{2}\Big)t$$ $$t=\frac{2s}{v+v_0}=\frac{2\times48}{26}=3.69s$$ So, $$\overline P=\frac{W}{t}=1.69\times10^4W$$
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