1 trolley with a mass of 2 kg moves at a speed of 1 m / s, a trolley with a mass of 1 kg moves towards it

1 trolley with a mass of 2 kg moves at a speed of 1 m / s, a trolley with a mass of 1 kg moves towards it, at a speed of 3 m / s. After an elastic impact, the trolleys move together. Find the direction and overall speed of movement

When the carts collide, the impulse conservation law arises: “the sum of the impulses of all bodies in the system remains unchanged for any interactions of bodies with each other.”

Before the collision of the carts: p1 = m1 * v1, p2 = – m2 * v2. The “-” sign appeared due to the opposite movement of the carts.

After impact: p = – (m1 + m2) * v. The “-” sign appeared due to the fact that the momentum of the second body is greater, which means that both carts after the collision will roll in the direction of movement of the second carriage.

According to the law of conservation of momentum: p1 + p2 = p => m1 * v1 – m2 * v2 = – (m1 + m2) * v

Let us express the unknown v from the resulting formula.

v = (m1 * v1 – m2 * v2) / – (m1 + m2)

v = (2 kg * 1 m / s – 1 kg * 3 m / s) / – (2 kg + 1 kg) = 1/3 m / s – the total speed of movement.

The direction of movement is determined by the body’s greatest momentum before the collision. So, the second cart has more impulse, because of which the system of bodies will move along the trajectory of the second cart, against the X axis.