A spring-loaded gun shoots the ball vertically upwards to a height of 30 cm if the spring is compressed for 1 s.

A spring-loaded gun shoots the ball vertically upwards to a height of 30 cm if the spring is compressed for 1 s. What is the stiffness of the spring if the mass of the ball of the ball is 15g.

Potential energy of the ball at a height of h = 30 cm = 0.03 m:

Ep = mgh,

where m is the mass of the ball, m = 15 g = 0.015 kg;

g – acceleration due to gravity, g = 9.81 m / s2.

The work performed when the spring is stretched with a stiffness k:

A = k x ^ 2/2,

where x = 1 cm = 0.01 m is the preliminary compression of the spring.

Equating En and A with each other, we get:

mgh = k x ^ 2/2, whence the stiffness of the spring:

k = 2mgh / x2.

Substitute all values in SI units:

k = 2 × 0.015 × 9.81 × 0.3 / 0.01 ^ 2 = 882.9 N / m.

Answer: k = 882.9 N / m.