Question

A $0.5Kg$ mass slides with uniform velocity down a rough inclined plane inclined to the horizontal at ${30}^o$. It slides from rest down the same plane but now inclined at ${40}^o$ to the horizontal. What velocity will it attain on sliding a distance of $2m$? $\left(78.56m/s\right)$

Answer 1

As the mass slides down with uniform velocity with plane inclined at ${30}^0$

$\mu =tan30=0.5773$

For plane inclined at ${40}^0$.

The force up the plane=$\mu mgcos40$

and force down the plane$=mgsin40$

Hence the net downward force=$mgsin40-\mu mgsin40$

Hence the downwards acc=$gsin40-\mu gsin40=1.965m/s^2$

Applying the equation.

$v^2=u^2+2as=0+2\times 1.965\times 2=7.86$

Hence the velocity=$2.804m/s$