Question

A solid bowling ball with a mass of 6.8 kilograms is rolling without slipping along a...

A solid bowling ball with a mass of 6.8 kilograms is rolling without slipping along a flat surface at a linear speed of 7.6 m/s. The ball has a diameter of 8.5 inches. If instead of pins, it encounters a long spring with a spring constant of 9300 N/m that has been attached to a wall ahead of it, what is the maximum it can compress the spring as it stops rolling.

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Answer #1

Moment of inertia of a solid ball, I = 2/5 MR2

Angular velocity, w = (Linear velocity)/radius = v/R

Rotational kinetic energy

Linear kinetic energy = 0.5*M*v2

Total kinetic energy = (1/5+1/2)Mv2 = 0.7Mv2

The potential energy stored in a spring, of spring constant K due to compression of x is = 0.5*K*x2

By the conservation of energy  

The spring can compress maximum 24 cm

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