Determine what kinetic energy will be obtained for two colliding balls with the same mass, equal to 4.0 kg

Determine what kinetic energy will be obtained for two colliding balls with the same mass, equal to 4.0 kg, if they were moving towards each other at speeds of 3.0 m / s and 8.0 m / s, and the impact was direct and inelastic?

m1 = m2 = 4 kg.

V1 = 3 m / s.

V2 = 8 m / s.

Ek -?

After an inelastic impact, the colliding balls will move at the same speed V.

The kinetic energy of the balls after collision Ek is determined by the formula: Ek = (m1 + m2) * V2 / 2.

For direct inelastic impact, the law of conservation of momentum is valid in vector form: m1 * V1 + m2 * V2 = (m1 + m2) * V.

Since the balls before the collision move towards each other, then for projections the law will have the form:

m1 * V1 – m2 * V2 = (m1 + m2) * V.

V = (m1 * V1 – m2 * V2) / (m1 + m2).

V = (4 kg * 3 m / s + 4 kg * 8 m / s) / (4 kg + 4 kg) = – 2.5 m / s.

The “-” sign indicates that after the impact the balls will move towards the ball, the velocity of which before the impact was V2 = 8 m / s.

Ek = (4 kg + 4 kg) * (8 m / s) 2/2 = 256 J.

Answer: after the collision, the balls will have kinetic energy Ek = 256 J.