Question

A solid cylinder rolls up an inclined plane of inclination theta with an initial velocity v. How far does the cylinder go up the plane ?

Answer 1

Answer:

(a) Let the cylinder roll up to height h.

From conservation of energy between the initial and final states,

21mv2+21Iω2=mgh

and, I=21mr2

⟹21mv2+21(21mr2)ω2=mgh

Also for rolling, v=rω

Thus h=4g3v2=1.913m

If s is distance it goes up the plane, sinθ=sh

Thus s=sinθh=3.826m

(b) Time taken to return the bottom=gsinθ2s(1+r2K2)=9.8×21