Question

In the figures (a) and (b) $AC,DG$ and $GF$ are fixed inclined planes, $BC=EF=x$ and $AB=DE=y$. A small block of mass $M$ is released from the point $A$. It slides down $AC$ and reaches $C$ with a speed $v_C$. The same block is released from rest from the point $D$. It slides down $DGF$ and reaches the point $F$ with speed $v_F$. The coefficients of kinetic frictions between the block and both the surfaces $AC$ and $DGF$ are $\mu$. Calculate $v_C$ and $v_F$.

Answer 1

In both the cases work done by friction will be $-\mu Mgx$.
$\therefore \frac{1}{2}M{v}_C^2=\frac{1}{2}M{v}_F^2=Mgy-\mu Mgx$
$\therefore v_C=v_F=\sqrt{2gy-2\mu gx}$