Question

The friction coefficient between the table and the block shown in figure (6-E4) is 0.2. Find the tensions in the two strings.

Answer 1

From the free body diagrams,
$T+15a-15g=0\Rightarrow T=15g-15a$
Now $T_1-5g-5a=0\Rightarrow T_1=5g+5a$
Again $T-(T_1+5a+mR)=0\Rightarrow T-(5g+5a+5a+mR)=0$
From equation (i) and (ii),
$15g-15a=5g+10a+0.2\left(5g\right)\Rightarrow 25a=+90\Rightarrow a=3.6m/s^2$
From equation(ii)
$T=5\times 10+10\times 3.6+0.2\times 5\times 100$
96 N in the left string
From equatiton (iii)
$T=5g+5a=5\times 10+5\times 36=50+18=68$ N in the left string