Question

a block of mass m is projected up an inclined plane of inclination theta with an initial velocity u.if the coefficient of kinetic friction between the block and plane is mu,the distance up to which the block will rise up the plane before coming to rest?

Answer 1

$$\begin{gathered} Whenobjectistakenupthroughaninclinedplanethennetforceactingonanobjectis: \\ F=mg\sin \theta +fr \\ wherefristhefrictionalforce \\ F=mg\sin \theta +\mu mg\cos \theta \\ ma=mg\sin \theta +\mu mg\cos \theta \\ a=g\sin \theta +\mu g\cos \theta \\ sothisistheaccelerationofthebody. \\ Initialspeedisu,finalspeediszero. \\ v=0 \\ dis\tan cetarvelledis: \\ {v}^2-u^2=2as \\ -u^2=2(g\sin \theta +\mu g\cos \theta )s \\ s=\frac{-u^2}{2\left(g\sin \theta +\mu g\cos \theta \right)} \\ Negativesignstatesthataccelerationisinthedirectionoppositetothedisplacementofthebody. \end{gathered}$$