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?

Open in App

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 $W_{f r} = - k m g cos α s = \frac{- k m v_{0}^{2}}{2 (k + tan α)}$

Suggest Corrections

Similar questions

Q. A disc of mass

50 g

slides with zero initial velocity down an inclined plane set at an angle

30^{\circ}

to the horizontal. Having traversed a distance of

50 c m

along the horizontal plane, the disc stops. The work performed by the friction forces over the whole distance, assuming the friction coefficient

0.15

for both inclined and horizontal planes is

(g = 10 m / s^{2})

Q. A disc of mass

m = 50 g

slides with the zero initial velocity down an inclined plane set at an angle

α = 30^{\circ}

to the horizontal; having traversed the distance

l = 50 c m

along the horizontal plane,the disc stops. If the work performed by the friction forces over the whole distance, assuming the friction coefficient

k = 0.15

for both inclined and horizontal planes is

\frac{x}{100} J

. Find

x

. (Write the answer to nearest integer)

Q. A block slides with constant velocity on a plane inclined at an angle

θ

. The same block is pushed up the plane with an initial velocity

v_{0}

. The distance covered by the block before coming to rest is :-

A body is moving up an inclined plane of angle $θ$ with an initial kinetic energy E. The coefficient of friction between the plane and the body is $μ$ . The work done against friction before the body comes to rest is

Q. A block slips with a constant velocity on a plane inclined at an angle

θ^{0}

. The same block is pushed up the plane with an initial velocity

v_{0}

. The distance covered by the block before coming to rest is-

Join BYJU'S Learning Program

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?