Two balls weighing 1 kg and 3 kg are moving towards each other at speeds of 4 m / s and 8 m / s

Two balls weighing 1 kg and 3 kg are moving towards each other at speeds of 4 m / s and 8 m / s, respectively. The amount of heat released after an absolutely inelastic collision of balls will be.

m1 = 1 kg.

m2 = 3 kg.

V1 = 4 m / s.

V2 = 8 m / s.

Q -?

The amount of thermal energy Q, which will be released upon impact, is expressed according to the law of conservation of energy: Q = Ek1 – Ek2, where Ek1 is the kinetic energy of two balls before the collision, Ek2 is the kinetic energy of two balls after the collision.

Ek1 = m1 * V1 ^ 2/2 + m2 * V2 ^ 2/2.

Ek1 = 1 kg * (4 m / s) ^ 2/2 + 3 kg * (8 m / s) ^ 2/2 = 104 J.

With an absolutely inelastic impact, the law of conservation of momentum is valid, and after the impact, the balls will move at the same speed.

m2 * V2 – m1 * V1 = (m1 + m2) * V.

V = (m2 * V2 – m1 * V1) / (m1 + m2).

V = (3 kg * 8 m / s – 1 kg * 4 m / s) / (1 kg + 3 kg) = 5 m / s.

Ek2 = (m1 + m2) * V ^ 2/2.

Ek2 = (1 kg + 3 kg) * (5 m / s) ^ 2/2 = 50 J.

Q = 104 J – 50 J = 54 J.

Answer: with an absolutely inelastic impact, Q = 54 J of thermal energy is released.