A ball with a mass flying at a speed of 4 m / s, upon impact, compresses the spring

A ball with a mass flying at a speed of 4 m / s, upon impact, compresses the spring. Find the stiffness of the spring if its compression turned out to be 4 cm.

Given:

m is the mass of the ball;

v = 4 m / s – ball speed;

dx = 4 centimeters = 0.04 meters – compression of the spring after being hit with a flying ball.

It is required to determine the stiffness of the spring k (N / m).

The flying ball has kinetic energy E:

E = m * v ^ 2/2.

After the impact, all the kinetic energy of the ball will be converted into the potential energy of the compressed spring W:

W = E;

k * dx ^ 2/2 = m * v ^ 2/2;

k * dx ^ 2 = m * v ^ 2

k = m * v ^ 2 / dx ^ 2 = m * 4 ^ 2 / 0.04 ^ 2 = m * 16 / 0.0016 = 10000 * m Newton / meter.

Answer: the stiffness of the spring is 10,000 * m Newton / meter.