Question

A uniform solid sphere with a mass of M = 360 grams and a radius R = 18.0 cm is rolling without slipping on a horizontal surface at a constant speed of 2.50 m/s. It then encounters a ramp inclined at an angle of 17.0 degrees with the horizontal, and proceeds to roll without slipping up the ramp. Use g = 10.0 m/s². How far does the sphere travel up the ramp (measure the distance traveled along the incline) before it stops for an instant?

Answer 1

here,

the mass of uniform solid sphere , m = 360 g = 0.36 kg

radius , R = 18 cm = 0.18 m

the initial velocity , u = 2.5 m/s

theta = 17 degree

let the distance traveled up the incline be s

using conservation of energy

0.5 * m * u^2 + 0.5 * I* w0^2 = m * g * (s * sin(theta))

0.5 * m * u^2 + 0.5 * (0.4 * m * r^2) * (u/r)^2 = m * g * (s * sin(theta))

0.5 * m * u^2 + 0.5 * (0.4 * m ) * (u)^2 = m * g * (s * sin(theta))

0.7 * u^2 = g * (s * sin(theta))

0.7 * 2.5^2 = 9.81 * (s * sin(17))

solving for s

s = 1.53 m

the distance traveled up the incline is 1.53 m