Question

Two smooth blocks of masses m and m' connected by a light inextensible string are moving on a smooth wedge of mass M. If a force F acts on the blocks. Find the (a) acceleration of the wedge and (b) value of F.

Answer 1

(a)From the free body diagram,

$R=m^{\prime }a...\left(1\right)$

$F-R=Ma$

Substituting in (1)

$F-m^{\prime }a=Ma$

Thus,

$(m^{\prime }+M)a=F$

$a=F/(m^{\prime }+M)$

(b)

Now to find $F$ such that the blocks don't move.

The force of tension $T$ acts on $m$.

Thus,

$T=ma$

and

$T=m^{\prime }g$ as the block of mass $m$ has no vertical acc.

Thus,

$ma=m^{\prime }g$

$a=m^{\prime }g/m$

Substituting the values of $F$ from the previous question.

$\frac{m^{\prime }g}{m}=\frac{F}{(m^{\prime }+M)}$

Hence,

$F=\frac{m^{\prime }g(m^{\prime }+M)}{m}$