Question

Figure shows two blocks tied by a string. A variable force $F=5t$ is applied on the block A. The coefficient of friction for the blocks A and B are $0.5$ and $0.6$ respectively. Find the tension in the string at time $t=2\text{sec}$ (in newtons)

Answer 1

The FBD of the blocks are as shown


At $t=2s$, $F=5t=5\times 2=10\text{N}$
From the FBD, we have
$N_A=20\text{N}$
$N_B=10\text{N}$
Maximum value of friction force on A is
$f_{Amax}=\mu N_A=0.5\times 20=10N$

So, at $t=2s$, $F=f_{Amax}$
Thus, the system will be at rest.
Hence, $f_A$ will be equal to $F$ i.e. $10\text{N}$
Therefore,
$T+f_A=F\Rightarrow T=0$