Question

A body of mass m is pushed with the initial velocity `v_0` up an inclined plane set at an angle `alpha` to the horizontal. The friction coefficient is equal to k. What distance will the body cover before it stops and what work do the friction forces perform over this distance?

Answer 1

Let s be the sought distance, then from the equation of increment of M.E. `DeltaT+DeltaU=A_(f r)`
`(0-1/2mv_0^2)+(+mgssin alpha)=-kmg cos alphas`
or, `s=(v_0^2)/(2g)//(sin alpha+kcos alpha)`
Hence `A_(f r)=-kmgcos alphas=(-kmv_0^2)/(2(k+tan alpha))`