Question

In the figures (a) and (b) $A C, D G$ and $G F$ are fixed inclined planes, $B C=E F=x$ and $A B=D E=y$. A small block of mass $M$ is released from the point $A$. It slides down $A C$ and reaches $C$ with a speed $v_{C}$. The same block is released from rest from the point $D$. It slides down $D G F$ and reaches the point $F$ with speed $v_{F}$. The coefficients of kinetic frictions between the block and both the surfaces $A C$ and $D G F$ are $\mu$. Calculate $v_{C}$ and $v_{F}$.

Answer 1

In both the cases work done by friction will be $-\mu M g x$.
$ \therefore \frac{1}{2} M v_{C}^{2} =\frac{1}{2} M v_{F}^{2}=M g y-\mu M g x$
$ \therefore v_{C} =v_{F}=\sqrt{2 g y-2 \mu g x}$