A ball weighing 40 g is rolled onto a spring at a speed of 1 m / s. How much will the spring length

A ball weighing 40 g is rolled onto a spring at a speed of 1 m / s. How much will the spring length decrease during compression if the spring rate is 50 N / m?

Let’s designate given: m = 40 g = 0.04 kg, v = 1 m / s, k = 50 H / m, dx-?

In this problem, the law of conservation of energy is fulfilled, at which all the kinetic energy of the ball is converted into the potential energy of the spring.

Ball kinetic energy Ek = m * v ^ 2/2

Spring potential energy Ep = k * dx

Ek = Ep => m * v ^ 2/2 = k * dx

dx = m * v ^ 2 / (2 * k) = 0.04 kg * (1 m / s) ^ 2 / (2 * 50 N / m) = 0.0004 m = 0.4 mm