Two carts with masses m1 = 3 kg and m2 = 1 kg are moving at speeds V1 = 2 m / s and V2 = 2 m / s towards each other

Two carts with masses m1 = 3 kg and m2 = 1 kg are moving at speeds V1 = 2 m / s and V2 = 2 m / s towards each other. Determine the amount of heat that will be released during the inelastic collision of the carts.

The released amount of heat:

Q = Ek1 + Ek2 – Ek1,2.

Ek1 = m1 * V1 ^ 2/2, Ek2 = m2 * V2 ^ 2/2, Ek1,2 = (m1 + m2) * V2 / 2.

Let us calculate the speed of the carts after inelastic collision:

m1V1 – m2V2 = (m1 + m2) * V.

V = (m1V1 – m2V2) / (m1 + m2) = (3 * 2 – 1 * 2) / (1 + 3) = (6 – 2) / 4 = 4/4 = 1 m / s.

Q = Ek1 + Ek2 – Ek1,2 = m1 * V1 ^ 2/2 + m2 * V2 ^ 2/2 – (m1 + m2) * V2 / 2 = 3 * 2 ^ 2/2 + 1 * 2 ^ 2 / 2 – (3 + 1) * 1 ^ 2/2 = 6 + 2 – 2 = 6 J.

Answer: 6 J of heat will be released.