# The spring of a children’s pistol, the stiffness of which is 10 N / cm, has a length of 15 cm.

**The spring of a children’s pistol, the stiffness of which is 10 N / cm, has a length of 15 cm. To what height will a ball weighing 10 g, fired from the pistol vertically upward, rise if the spring was compressed to 5 cm? Neglect air resistance.**

Given:

k = 10 N / cm = 1000 N / m – the stiffness of the spring of the child’s pistol;

L = 15 centimeters = 0.15 meters – the length of the spring of the child’s pistol;

L1 = 5 centimeters = 0.05 meters – the length of the spring after compression;

m = 10 grams = 0.01 kilograms is the mass of the ball fired from the pistol;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine H (meter) – the height to which the ball released vertically upwards will rise.

Let’s find the potential energy of the compressed spring:

E = k * dx ^ 2/2 = k * (L – L1) ^ 2/2 = 1000 * (0.15 – 0.05) ^ 2/2 =

= 1000 * 0.1 ^ 2/2 = 1000 * 0.01 / 2 = 500 * 0.01 = 5 Joules.

When fired, this potential energy will first go into the kinetic energy of the ball, and then into the potential energy of the ball, that is:

E = m * h * g;

h = E / (m * g) = 5 / (0.01 * 10) = 5 / 0.1 = 50 meters.

Answer: the ball will rise to a height of 50 meters.