Question

a hollow ball is rolling along a horizontal surface at 2.8 m/s when it encounters an upward incline. part a if it rolls without slipping up the incline, what maximum height will it reach? express your answer using two significant figures.

Answer 1

E = 1/2 I ω^2 + 1/2 M V*2 total kinetic energy of ball

E = 1/2 M R^2 * (V / R)^2 + 1/2 M V^2 = M V^2 total KE of rolling ball

F = 1/2 M g sin θ force acting down incline of ball

F h = E where h is the distance in height thru which F must act

M V^2 = 1/2 L M g sin θ = 1/2 h M g (since h = L * sin θ)

h = 2 * V^2 / g maximum height of ball on incline of θ

h = 2 * (2.8 m/s)^2 / 9.80 m/s^2 = 1.6 m