Question

Consider a bowling ball rolling without slipping up a hill. a) Find how high up this inclined surface the ball rolls if the ball was rolling at 2.5 m/s at the bottom of the hill. b) Would a volleyball moving at 2.5 m/s roll further up this than a bowling ball? Explain. c) Would the bowling ball move further up the hill if it were sliding without friction instead of rolling? Explain.

Answer 1

here,

a)

initial speed of the ball , v = 2.5 m/s

let the height on incline be h

using conservation of energy

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 = m*g*h

0.7 * v^2 = g*h

0.7 * 2.5^2 = 9.8 * h

h = 0.45 m

the height reached is 0.45 m

b)

taking volley ball as a hollow sphere

moment of inertia of volley ball , I = 0.67 *m*r^2

therefore,

let the height on incline be h

using conservation of energy

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

0.5 * (0.67 * m*r^2) * (v/r)^2 + 0.5 *m*v^2 = m*g*h

0.835 * v^2 = g*h

0.835 * 2.5^2 = 9.8 * h

h = 0.53 m

the height reached by the volleyball is 0.53 m

c)

if the bowling ball is sliding without rolling,

then the initial kinetic energy is decreased

and initial kinetic energy is converted into the potential energy

so the bowling ball move further less on the incline