Question

A system consists of Block $A$ and $B$ of masses $5\text{kg}$ each and connected to a pulley as shown in figure. Find the minimum value of force $F$ at which they will start moving? (Assume $g=10{\text{m/s}}^2$).

• A. $60\text{N}$
• B. $30\text{N}$
• C. $120\text{N}$
• D. $90\text{N}$

Answer 1

The correct option is A $60\text{N}$

Let us find the forces acting on each block, so the FBDs of the blocks are as shown



From the FBDs we have
$N_1=5g=50\text{N}$
The static friction between block $A$ and $B$ is
$f_{2s}={\mu }_{2s}\left(N_1\right)=0.6\left(50\right)=30\text{N}$

Now, as per the question, the blocks just start moving, means, the friction will be limiting friction.

So, for block $B$:
$T=f_{2s}$
For block $A$:
$T+f_{2s}=F$
$\Rightarrow F=2f_{2s}=2\times 30=60\text{N}$
Hence, if the force $F$ is above $60\text{N}$, they will move.