A ball with a mass of 2 kg, moving at a speed of 1.2 m / s, strikes a ball with a mass of 1.5 kg at rest.

A ball with a mass of 2 kg, moving at a speed of 1.2 m / s, strikes a ball with a mass of 1.5 kg at rest. Calculate the speed of the balls after elastic interaction.

m1 = 2 kg.

V1 = 1.2 m / s.

m2 = 1.5 kg.

V2 = 0 m / s.

V1 “-?

V2 “-?

Let’s write down the law of conservation of momentum and total mechanical energy.

m 1 * V1 + m2 * V2 = m 1 * V1 “+ m2 * V2”.

m 1 * V12 / 2 + m2 * V22 / 2 = m 1 * V1 “2/2 + m2 * V2” 2/2.

m 1 * V1 = m 1 * V1 “+ m2 * V2”.

m 1 * V12 = m 1 * V1 “2 + m2 * V2” 2.

m 1 * V1 – m 1 * V1 “= m2 * V2”.

m 1 * V12 – m 1 * V1 “2 = m2 * V2” 2.

m 1 * (V1 – V1 “) = m2 * V2”.

m 1 * (V12 – V1 “2) = m2 * V2” 2.

m 1 * (V1 – V1 “) * (V1 + V1”) = m2 * V2 “2.

Divide the second equation by the first.

V1 + V1 “= V2”.

V2 “= V1 + V1”.

m 1 * V1 = m 1 * V1 “+ m2 * (V1 + V1”).

m 1 * V1 = m 1 * V1 “+ m2 * V1 + m2 * V1”.

m 1 * V1 – m2 * V1 = m 1 * V1 “+ m2 * V1”.

V1 “= V1 * (m 1 – m2) / (m 1 + m2).

V1 “= 1.2 m / s * (2 kg – 1.5 kg) / (2 kg + 1.5 kg) = 0.17 m / s.

V2 “= 1.2 m / s + 0.17 m / s = 1.37 m / s.

Answer: V1 “= 0.17 m / s, V2” = 1.37 m / s.