Question

A ball of mass m and radius r rolls at speed v into a spring with constant k. How much does it compress the spring?

a) (mv²)/(2k)
b) (mv²)/k
c) (mv²)/(4k)
d) (mv²)/(8k)

Answer 1

The compression of the spring can be determined using the equation (mv²)/(2k), where m is the mass of the ball, v is the speed of the ball, and k is the spring constant.

Step-by-step explanation:

The compression of the spring can be determined using the principle of conservation of mechanical energy. When the ball rolls into the spring, its initial kinetic energy is converted into potential energy stored in the compressed spring, as well as rotational kinetic energy of the ball. The equation for the compression of the spring is given by:

(mv²) / (2k)

where m is the mass of the ball, v is the speed of the ball, and k is the spring constant.