Question

A solid sphere is rolling along a level surface with a translational velocity of 17.5 m/s. What is the final height of the object if it then rolls up an inclined plane?

Answer 1

here,

the mass of solid sphere is m and radius is r

intial translational speed , u = 17.5 m/s

let the final height ogf the object if it then roll up the incline be h

using conservation of energy

inital translational kinetic energy + inital rotational energy = final potential energy

0.5 * m * v^2 + 0.5 * I * w^2 = m * g * h

0.5 * m * v^2 + 0.5 * ( 0.4 * m* r^2 ) * ( v/r)^2 = m * g * h

0.7 * v^2 = g * h

0.7 * 17.5^2 = 9.81 * h

solving for h

h = 21.9 m

the final height of the object if it then roll up the incline is 21.9 m