Determine the speed of a ball weighing 5 g at the moment of firing from the barrel of a spring pistol

Determine the speed of a ball weighing 5 g at the moment of firing from the barrel of a spring pistol, if the spring rate is 200 N / m, and before firing it was compressed by 6 cm.

m = 5 grams = 0.005 kilograms – the mass of the ball;

k = 200 Newton / meter – coefficient of stiffness of the pistol spring;

dx = 6 centimeters = 0.06 meters – the amount of compression of the spring.

It is required to determine the speed of the ball at the moment of the shot v (m / s).

The potential energy of a compressed spring is:

W = k * dx ^ 2/2 = 200 * 0.06 ^ 2/2 = 100 * 0.06 ^ 2 = 100 * 0.0036 = 0.36 Joule.

Since the condition of the problem does not indicate the opposite, we assume that all the potential energy of the compressed spring has passed into the kinetic energy of the ball’s motion. Then:

W = m * v ^ 2/2

v = (2 * W / m) ^ 0.5 = (2 * 0.36 / 0.005) ^ 0.5 = (0.72 / 0.005) ^ 0.5 = (144) ^ 0.5 = 12 m /from.

Answer: the speed of the ball will be 12 meters per second.