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 210: 95a

Answer

$v = 5.5~m/s$

Work Step by Step

We can find the speed at the bottom of the ramp: $K_1+U_1+W = K_2+U_2$ $0+U_1+W = K_2+0$ $K_2 = U_1+W$ $\frac{1}{2}mv^2 = mgh-F_f~L$ $v^2 = \frac{(2)(mgh-F_f~L)}{m}$ $v^2 = \frac{(2)(mgL~sin~\theta-L~mg\mu_k~cos~\theta)}{m}$ $v^2 = (2)(gL~sin~\theta-L~g\mu_k~cos~\theta)$ $v = \sqrt{(2)(gL~sin~\theta-L~g\mu_k~cos~\theta)}$ $v = \sqrt{(2)[(9.8~m/s^2)(3.7~m)~(sin~39^{\circ})-(3.7~m)~(9.8~m/s^2)(0.28)~(cos~39^{\circ})]}$ $v = 5.5~m/s$
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