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 - Page 212: 126b

Answer

$v = 1.9~m/s$

Work Step by Step

We can find the height $h$ above the lowest point when the angle is $30.0^{\circ}$: $\frac{L-h}{L} = cos~\theta$ $L-h = L~cos~\theta$ $h = L~(1-cos~\theta)$ $h = (1.4~m)~(1-cos~30.0^{\circ})$ $h = 0.19~m$ The kinetic energy at the lowest point is equal to the potential energy at the highest point: $\frac{1}{2}mv^2 = mgh$ $v^2 =2gh$ $v =\sqrt{2gh}$ $v =\sqrt{(2)(9.8~m/s^2)(0.19~m)}$ $v = 1.9~m/s$
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