University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 7 - Potential Energy and Energy Conservation - Problems - Exercises - Page 231: 7.38

Answer

The mass of the heavier block is 15.1 kg. The mass of the lighter block is 6.9 kg

Work Step by Step

Let $m_1$ be the mass of the heavier block. Let $m_2$ be the mass of the lighter block. Note that $m_2 = 22.0~kg-m_1$ Let $U_1 = 0$ $K_1+U_1 = K_2+U_2$ $0+0= \frac{1}{2}(m_1+m_2)v^2-m_1gh+m_2gh$ $0= \frac{1}{2}(m_1+m_2)v^2-m_1gh+(22.0~kg)gh - m_1gh$ $2m_1gh = \frac{1}{2}(m_1+m_2)v^2+(22.0~kg)gh$ $m_1 = \frac{\frac{1}{2}(m_1+m_2)v^2+(22.0~kg)gh}{2gh}$ $m_1 = \frac{\frac{1}{2}(22.0~kg)(3.00~m/s)^2+(22.0~kg)(9.80~m/s^2)(1.20~m)}{(2)(9.80~m/s^2)(1.20~m)}$ $m_1 = 15.1~kg$ The mass of the heavier block is 15.1 kg. The mass of the lighter block is 22.0 kg - 15.1 kg, which is 6.9 kg
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