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 $T=281N$
