A body weighing 1 kg freely falls from a height of 20 meters onto a vertically standing spring.

A body weighing 1 kg freely falls from a height of 20 meters onto a vertically standing spring. On impact, the spring is compressed by L = 0.1 meter. Determine the stiffness of the spring.

To determine the stiffness of a vertically standing spring, we use the equality: m * g * h = En (potential energy) = k * Δx ^ 2/2, whence we express: k = 2 * m * g * h / Δx ^ 2.

Constants and variables: m – mass of the fallen body (m = 1 kg); g – acceleration due to gravity (g ≈ 10 m / s2); h – fall height (h = 20 m); Δx – compression on impact (Δx = 0.1 m).

Calculation: k = 2 * m * g * h / Δx ^ 2 = 2 * 1 * 10 * 20 / 0.1 ^ 2 = 40 * 10 ^ 3 N / m = 40 kN / m.

Answer: The stiffness of a vertically standing spring is 40 kN / m.