# What speed will a projectile weighing 0.1 kg acquire under the action of a spring of 90 N / m compressed by 3 cm?

August 18, 2021 | education

| Given:

k = 90 N / m – coefficient of spring stiffness;

dx = 3 centimeters = 0.03 meters – the amount of compression of the spring;

m = 0.1 kilogram is the mass of the projectile.

It is required to determine the speed of the projectile v.

Since it is not specified in the condition of the problem, he believes that the potential energy of the compressed spring will completely transform into the kinetic energy of the projectile. Then, according to the law of conservation of energy:

Epot = Ekin;

k * dx ^ 2/2 = m * v ^ 2/2;

k * dx ^ 2 = m * v ^ 2;

v = (k * dx ^ 2) ^ 0.5 / m = dx * k ^ 0.5 / m = 0.03 * 90 ^ 0.5 / 0.1 =

= 0.03 * 9.5 / 0.1 = 0.3 / 0.1 = 3 m / s.

Answer: under the action of a spring, the projectile will acquire a speed of 3 m / s.

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