A solid sphere is rolling smoothly with a speed of 6.0 m/s on a horizontal surface. It then rolls up a ramp to a maximum height of h and stops. Calculate this maximum height. (The moment of inertia of a solid sphere is I

Explanation:

This exercise we will work using energy conservation, let's use two points

 lower. Ramp starting point

        Em₀ = K = ½ m v² + ½ I w²

more height. Point where e stops

        = m g h

at the starting point the sphere is spinning let's look for the relationship between the angular and linear variables

        v = w r

the moment of inertia of a sphere is tabulated

         I = 2/5 M R2

let's use that energy is conserved

        Em₀ = Em_{f}

        ½ m v² + ½ (2/5 m r²) (v / r)² = m g h

        ½ v² + 1/5 v2 = g h

        h= 7/10 v² / g