Question

A block of mass $m$ slides in an inclined right angled trough as shown in figure. If coefficient of kinetic friction between block and material composing the trough is ${\mu }_k$, find the acceleration of the block.

Answer 1

Substitute $N=\frac{mg\cos \theta }{\sqrt{2}}$ in equation $mg\sin \theta -2{\mu }_{k}N=ma$

$mg\sin \theta -2{\mu }_k\left(\frac{mg\cos \theta }{\sqrt{2}}\right)=ma$

$a=g\sin \theta -\sqrt{2}{\mu }_{k}g\cos \theta$

Therefore the acceleration of block given $a=g\sin \theta -\sqrt{2}{\mu }_{k}g\cos \theta$