## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson

# Chapter 7 - Newton's Third Law - Exercises and Problems - Page 190: 55

#### Answer

The acceleration of the 2.0-kg block is $3.27~m/s^2$.

#### Work Step by Step

We can set up a force equation for the 1.0-kg block. Let $m_2$ be the mass of this block. Let $T$ be the tension in the rope; $\sum F = m_2~a_2$ $m_2~g - T = m_2~a_2$ $T = m_2~g - m_2~a_2$ We can use this expression for the tension $T$ in the force equation for 2.0-kg block. Let $m_1$ be the mass of this block. Note that $a_2 = 2a_1$. $\sum F = m_1~a_1$ $2T = m_1~a_1$ $2m_2~g - 2m_2~a_2 = m_1~a_1$ $2m_2~g - 2m_2~(2~a_1) = m_1~a_1$ $2m_2~g = m_1~a_1+4m_2~a_1$ $a_1 = \frac{2m_2~g}{m_1+4m_2}$ $a_1 = \frac{(2)(1.0~kg)(9.80~m/s^2)}{2.0~kg+(4)(1.0~kg)}$ $a_1 = 3.27~m/s^2$ The acceleration of the 2.0-kg block is $3.27~m/s^2$.

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