Question:
The friction coefficient between the table and the blockshown in figure is $0.2$. Find the tensions in the two strings.
Solution:
$15 g-T=15 a \quad-(i)$
$T-T_{1}-\mu N=5 a \& \mu N=0.2 \times 5 g=g$
$T-T_{1}-g=5 a-(i i)$
$T_{1}-5 g=5 a \quad-(i i i)$
Adding (i), (ii) and (iii)
$15 g-g-5 g=15 a+5 a+50$
$9 q=25 a$
$a=\frac{9 g}{25}$
Now, put in eq.(i)
$T=15 g-15\left(\frac{9 g}{25}\right)$
$\mathrm{T}=96 \mathrm{~N}$
From eq.(3)
$T_{1}=5 g+5 \times \frac{9 g}{25}$
$T_{1}=68 \mathrm{~N}$