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?(1 point)
Responses
The momentum of each ball stays the same, and the total momentum stays the same.
The momentum of each ball stays the same, and the total momentum stays the same.
The momentum of each ball changes, and the total momentum changes.
The momentum of each ball changes, and the total momentum changes.
The momentum of each ball stays the same, and the total momentum changes.
The momentum of each ball stays the same, and the total momentum changes.
The momentum of each ball changes, and the total momentum stays the same.
The momentum of each ball changes, and the total momentum stays the same.
The correct answer is: The momentum of each ball changes, and the total momentum stays the same.
The correct statement is:
The momentum of each ball changes, and the total momentum stays the same.
To understand why this is the case, let's break down the problem step by step:
1. Initially, the first ball has a momentum of 24 kg·m/s and the second ball is at rest, so its momentum is 0 kg·m/s.
2. When the two balls collide, the first ball transfers some of its momentum to the second ball. This is a classic example of an elastic collision, where kinetic energy is conserved.
3. To find the final momentum of each ball, we need to apply the law of conservation of momentum. According to this law, the total momentum of any closed system remains constant if no external forces act on it.
4. In this closed system, the total initial momentum is given by the sum of the individual momenta: 24 kg·m/s + 0 kg·m/s = 24 kg·m/s.
5. Therefore, since the total momentum before the collision is 24 kg·m/s, it must also be 24 kg·m/s after the collision. This means that the total momentum stays the same.
6. However, since the initial momentum of the first ball is transferred to the second ball during the collision, the momentum of each ball changes. The first ball's momentum decreases, while the second ball's momentum increases.
So, the momentum of each ball changes, and the total momentum stays the same.