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Standard XII

Physics

Work Energy Theorem Application

A body of mas...

Question

A body of mass $m$ is pushed with the initial velocity $v_{0}$ up an inclined plane set at an angle $α$ 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?

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Solution

Let $s$ be the sought distance, then from the equation of increment of M.E. $Δ T + Δ U = W_{f r}$
$(0 - \frac{1}{2} m v_{0}^{2}) + (+ m g s sin α) = - k m g cos α s$
or, $s = \frac{\frac{v_{0}^{2}}{2 g}}{(sin α + k cos α)}$
Hence $W_{f r} = - k m g cos α s = \frac{- k m v_{0}^{2}}{2 (k + tan α)}$

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A body of mass m is pushed with the initial velocity v0 up an inclined plane set at an angle α 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?

Let s be the sought distance, then from the equation of increment of M.E. ΔT+ΔU=Wfr(0−12mv20)+(+mgssinα)=−kmgcosαsor, s=v202g(sinα+kcosα)Hence Wfr=−kmgcosαs=−kmv202(k+tanα)

A body of mass $m$ is pushed with the initial velocity $v_{0}$ up an inclined plane set at an angle $α$ 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?