Question

In the arrangement shown in $Fig.6.40$, the strings are light and inextensible. The surface over which blocks are placed is smooth.
Find:
$a$ the acceleration of each block
$b$. the tension in each string

Answer 1

$a$. Let a be the acceleration of each block and $T_1$ and $T_2$ be the tensions, in the two strings as shown in $Fig.6.41$.
Taking the three blocks and the two strings as the system.
Using $\sum F_x=m{a}_x$
or $28=(4+2+1)a$
or $a=\frac{28}{7}4m{s}^{-2}$
$b$. Free-body diagrams (showing the forces in x-direction only) of $4kg$ block and $1kg$ block are shown in $Fig.6.43$.
Using $\sum F_t=m{a}_t$
For $1kg$ block : $F-T=\left(1\right)$ (a)
or $28-T_1=\left(1\right)\left(4\right)=4$
$\Rightarrow$ $T_1=28-4=24N$
For $4kg$ blocks : $T_2=\left(4\right)$ (a)
$\Rightarrow$ $T_2=\left(4\right)\left(4\right)=16N$