Question

A child rolls a bowling ball of mass 4.10   kg up a long ramp. The bowling ball can be considered a solid sphere. When the child pushes up the bowling ball at the bottom of the ramp, it has a speed of 12.8 m/s .

Part A Part complete Find the maximum vertical height increase of the bowling ball as it rolls up the ramp. Assume that the bowling ball rolls without slipping.

Answer 1

here,

mass , m = 4.1 kg

initial speed of the ball at the bottom , u = 12.8 m/s

let the maximum vertical height increase be h

using conservation of mechanical energy

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

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

0.7 * u^2 = g * h

0.7 * 12.8^2 = 9.81 * h

solving for h

h= 11.7 m

the maximum vertical height increase is 11.7 m