A body of mass 4kg moving with a velocity of 10meter per second collide with a stationary body of mass 6kg. If the two body move together after the collision, calculate their common veoocity

Answer 1

To solve this problem, we can use the principle of conservation of momentum.

The momentum of an object is given by the product of its mass and velocity. It is conserved in a closed system, which means that the total momentum before the collision is equal to the total momentum after the collision.

The momentum before the collision can be calculated as:
Momentum1 = mass1 * velocity1 = 4 kg * 10 m/s = 40 kg·m/s

Since the second body is stationary, its initial velocity is 0, so its momentum is:
Momentum2 = mass2 * velocity2 = 6 kg * 0 m/s = 0 kg·m/s

The total momentum before the collision is the sum of the momenta of the two bodies:
Total momentum before = Momentum1 + Momentum2 = 40 kg·m/s + 0 kg·m/s = 40 kg·m/s

After the collision, the two bodies move together with a common velocity, which we'll call V.

The total mass after the collision is the sum of the masses of the two bodies:
Total mass = mass1 + mass2 = 4 kg + 6 kg = 10 kg

The total momentum after the collision is the product of the total mass and the common velocity:
Total momentum after = Total mass * Common velocity = 10 kg * V

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore,
Total momentum before = Total momentum after

40 kg·m/s = 10 kg * V

Divide both sides of the equation by 10 kg:
40 kg·m/s / 10 kg = V
4 m/s = V

Therefore, the common velocity of the two bodies after the collision is 4 m/s.