Two inelastic bodies, the mass of which is 2 and 6 kg, move towards each other at speeds of 2

Two inelastic bodies, the mass of which is 2 and 6 kg, move towards each other at speeds of 2 m / s each. With what speed and in what direction will these bodies move after impact?

Given:

m1 = 2 kilograms – the mass of the first body;

v1 = 2 m / s – the speed of the first body;

m2 = 6 kilograms – the mass of the second body;

v2 = 2 m / s – speed of movement of the second body.

It is required to determine the speed of motion of bodies v (m / s) and the direction of motion after an inelastic impact.

By the statement of the problem, both bodies are inelastic. Then, after the impact, they will move together as one. Let the first body move in the positive direction of the coordinate axis, and the second body in the negative direction. Then, according to the law of conservation of momentum:

m1 * v1 – m2 * v2 = (m1 + m2) * v;

v = (m1 * v1 – m2 * v2) / (m1 + m2) = (2 * 2 – 6 * 2) / (2 + 6) =

= (4 – 12) / 8 = -8 / 8 = -1 m / s.

The negative sign of the velocity indicates that the bodies are moving in the negative direction of the coordinate system (that is, in which the second body moved before impact).

Answer: the bodies will move at a speed of 1 m / s in the direction of the movement of the second body before the impact.