## Physics (10th Edition)

Published by Wiley

# Chapter 4 - Forces and Newton's Laws of Motion - Problems - Page 117: 83

#### Answer

(a) The acceleration of the objects is $3.56m/s^2$ (b) The tension in the string is $281N$

#### Work Step by Step

1) Consider the bigger object $(m_1=45kg)$ There are 2 forces acting on this object: - Its weight $m_1g=45\times9.8=441N$ - The opposite tension in the string $T$ As the object moves at acceleration $a$, we have $$m_1g-T=m_1a$$ $$441-T=45a\hspace{1cm}(1)$$ 2) Consider the smaller object $(m_2=21kg)$ There are also 2 forces acting on this object: - Its weight $m_2g=21\times9.8=205.8N$ - The opposite tension in the string $T$ (same as 1) 2 objects are connected, so they act as a system and both move at the same magnitude of $a$ $$T-m_2g=m_2a$$ $$T-205.8=21a\hspace{1cm}(2)$$ Solving (1) and (2), we have $a=3.56m/s^2$ and $T=281N$

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