In a closed system, a ball with a mass of 3 kg and a momentum of 24 kg·m/s collides into a ball with a mass of 1 kg that is originally at rest. Which statement describes the momentum of the balls and the total momentum?
In a closed system, the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity.
Before the collision, the first ball has a momentum of 24 kg·m/s and the second ball has a momentum of 0 kg·m/s (because it is at rest).
After the collision, the first ball collides into the second ball. Let's assume they stick together after the collision. In this case, the two balls will move together with a common velocity.
Let the final velocity of the two balls be v kg/s. The total momentum after the collision is the sum of the momentum of the first ball and the second ball, which is equal to the mass of the first ball (3 kg) multiplied by the final velocity (v), since the second ball is originally at rest.
Therefore, the total momentum before the collision equals the total momentum after the collision:
24 kg·m/s = (3 kg) * v
Solving the equation, we find that the final velocity (v) is equal to 8 m/s.
So, after the collision, the two balls will have a common velocity of 8 m/s. Since they are moving together, their momenta add up to give the total momentum of the system, which is:
(3 kg) * (8 m/s) + (1 kg) * (8 m/s) = 24 kg·m/s + 8 kg·m/s = 32 kg·m/s
Therefore, the momentum of the balls is 8 kg·m/s and the total momentum of the system is 32 kg·m/s.