Question

'A bowling ball is released from rest at the top of an inclined plane that is h=1 m high. The ball has a mass m=10kg and a radius of 0.1m. What is the linear speed of the ball when it gets to the bottom of the ramp if it rolls without slipping?

Answer 1

here,

the height of incline , h = 1 m

the mass of ball , m = 10 kg

radius , r = 0.1 m

let the linear speed of the ball at the bottom of ramp be v

using conservation of energy

initial mechanical energy = final mechanical energy

PEi = KEr + KEt

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

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

g * h = 0.7 * v^2

9.81 * 1 = 0.7 * v^2

solving for v

v= 3.74 m/s

the linear speed of the ball when it gets to the bottom of the ramp if it rolls without slipping is 3.74 m/s