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 206: 55c

Answer

$v =1.04m/s$

Work Step by Step

The energy from the speed and friction of the block is converted to the energy used in compressing the spring $\Delta K + E_{th} =E_s $ $(K_{_2}-K_{_1}) + E_{th} =E_s $ $\frac{1}{2}m(v_{_2}-v_{_1}) = E_s- E_{th} $ $\frac{1}{2}m(v_{_2}^2-v_{_1}^2) = E_s- E_{th} $ $v_{_2}^2-v_{_1}^2 = \frac{2(E_s - E_{th})}{m}$ $-v_{_1}^2 = \frac{2(E_s - E_{th})}{m} -v_{_2}^2$ $-v_{_1}^2 = \frac{2(E_s - E_{th})}{m} -v_{_2}^2$ $v_{_1}^2 = -({\frac{2(E_s - E_{th})}{m} -v_{_2}^2})$ $v =\sqrt {-({\frac{2(E_s - E_{th})}{m} -v_{_2}^2})}$ $v =\sqrt {-({\frac{2(-0.9 - 0.46)}{2.5} -0^2})}$ $v =1.04m/s$
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