Question

A system is pushed by a force $F$ as shown in figure. All surfaces are smooth except between $B$ and $C$. Friction coefficient between $B$ and $C$ is $\mu$. Minimum value of $F$ to prevent block $B$ from down ward slipping is

Answer 1

Refer above image 1,2,3.

$f-N=2ma$........(i)

$\left(N\right)-\left(N^{\prime }\right)=ma$.......(ii)

$N^{\prime }=2ma$.........(iii)

So $N=3ma$ and $f=5ma$

Now

$a=\frac{f}{5m}$

Refer above image 4.

$(N-N^{\prime })u=fsmax$

$\Rightarrow \left(ma\right)u=5ma$

$(N-N^{\prime })=\frac{mg}{u}$

$(N-N^{\prime })=ma$

$\therefore ma=\frac{mg}{u}$

and $ma=\frac{f}{5}$

So $\frac{f}{5}=\frac{mg}{u}$

$\Rightarrow f=\frac{5mg}{u}$