A bullet flying horizontally hits a wooden block lying on a smooth table and gets stuck in it.

A bullet flying horizontally hits a wooden block lying on a smooth table and gets stuck in it. The mass of the bullet is m = 10g, the mass of the bar is M = 100g, and the speed of the bullet is 110m / s. Determine the kinetic energy of the bar with the bullet after the impact. Is the total mechanical energy saved in this case?

The momentum conservation equation:

m U = (m + M) V,

where m is the mass of the bullet, m = 10 g = 0.01 kg; U – bullet speed, U = 110 m / s; M is the mass of the bar, M = 100 g = 0.1 kg; V is the speed of the bar with the bullet.

V = m U / (m + M) = 0.01 × 110 / (0.01 + 0.1) = 10 m / s.

Bullet kinetic energy: Ek1 = m U ^ 2/2 = 0.01 × 110 ^ 2/2 = 60.5 J.

Kinetic energy of a bar with a bullet: Ek ^ 2 = (m + M) V ^ 2/2 = 0.11 × 10 ^ 2/2 = 5.5 J.

The total mechanical energy is reduced, the difference is converted into thermal energy.