Question

A ring (hollow cylinder) of mass 2.89kg, inner radius 5.35cm, and outer radius 6.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=35.6°, as shown in the figure below. At the moment the ring is at position x = 1.87m up the plane, its speed is 2.80m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

Answer 1

I would approach this as conservation of energy.
initialKE+InitialPE=final PE
first calculate the monent of inertia for the cylinder.

Then,
1/2 I v^2 r+mg d sinTheta+1/2 m vi^2=mg hfinal*sinTheta.
solvie for hfinal.