The carts move towards each other at speeds equal to 2 and 1.5 m / s. After the meeting, they push off and move

The carts move towards each other at speeds equal to 2 and 1.5 m / s. After the meeting, they push off and move in opposite directions at speeds of 1.5 and 2 m / s. What is the mass of the first cart if the mass of the second is 2 kg?

Given:

m2 = 2 kilograms – the mass of the second cart;

v1 = 2 meters per second – the speed of the first cart before interaction;

v2 = 1.5 meters per second – speed of the second cart before interaction;

v3 = 1.5 meters per second – the speed of the first cart after interaction;

v4 = 2 meters per second – the speed of the second cart after interaction.

It is required to determine m1 (kilogram) – the mass of the first cart.

Let the first cart initially move in the positive direction of the coordinate system, and the second in the negative. Then, according to the law of conservation of momentum (momentum), we obtain:

m1 * v1 – m2 * v2 = m2 * v4 – m1 * v3;

m1 * v1 + m1 * v3 = m2 * v2 + m2 * v4;

m1 * (v1 + v3) = m2 * (v2 + v4);

m1 = m2 * (v2 + v4) / (v1 + v3) = 2 * (1.5 + 2) / (2 + 1.5) =

= 2 * 3.5 / 3.5 = 2 kilograms.

Answer: the mass of the first cart is also 2 kilograms.