A mass m slides down a fixed plane inclined at an angle α to the horizontal. find the distance that it will move on the horizontal plane after covering the entire length of the inclined plane. the height of the plane is h and the coefficient of friction over both surfaces is μ.




This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Inclination angle = α
height of plane = h
friction coefficient = μ

Initial potential energy = mgh  (assuming horizontal plane to be of 0 potential energy)
Initial kinetic energy = 0
Final potential energy = 0
Final kinetic energy = 0
Thus change in energy = mgh

The energy is lost due to friction.

Length of inclined plane  = h.cosec(
let it travels a distance x on horizontal plane.
Energy lost due to friction = 
μ[mg.cos(α)(h.cosec(α)) + mg.x]

So mgh = μ[mg.cos(α)(h.cosec(α)) + mg.x]
⇒ mgh = μmg[cos(α)(h.cosec(α)) + x]
⇒h/μ = cos(α)(h.cosec(α)) + x
⇒h/μ = h.cot(α) + x
⇒x = h[1/μ - cot(α)]

Thus it will travel h[1/μ - cot(α)] on horizontal plane.