The bullet hits a body weighing 1.95 kg and gets stuck in it. The body is glued to the wall with a spring.

The bullet hits a body weighing 1.95 kg and gets stuck in it. The body is glued to the wall with a spring. Determine the deformation if the stiffness factor is 20 kilonewtons / meter. (muzzle velocity 100 m / s) (neglect friction)

m = 1.95 kg.

k = 20 kN / m = 20,000 N / m.

V0 = 100 m / s.

x -?

We will use the law of conservation of total mechanical energy.

The kinetic energy of the bullet Ek is converted into the potential energy of the compressed spring En.

Ek = En.

The kinetic energy of a bullet Ek is determined by the formula: Ek = m * V0 ^ 2/2.

The potential energy of a compressed spring is determined by the formula: En = k * x ^ 2/2.

m * V0 ^ 2/2 = k * x ^ 2/2.

x = √ (m * V0 ^ 2 / k).

x = √ (1.95 kg * (100 m / s) ^ 2 / 20,000 N / m) = 1 m.

Answer: the deformation of the spring when hit by a bullet is x = 1 m.