How to Calculate Momentum in a Pool Game Collision
What is the momentum of the green billiard ball right after the collision?
Josh is playing pool. During his shot, an orange billiard ball with a momentum of 135 g · m/s hits a green billiard ball at rest. After the collision, the orange billiard ball continues in the same direction with a momentum of 60 g · m/s. What is the momentum of the green ball right after the collision?
Answer:
The momentum of the green ball right after the collision is 0.075 kg · m/s.
When solving this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces are acting on the system.
Let's denote the momentum of the orange ball before the collision as p1, and the momentum of the green ball after the collision as p2.
Given:
- Initial momentum of the orange ball (p1) = 135 g · m/s
- Final momentum of the orange ball (p1') = 60 g · m/s
- Momentum of the green ball after the collision (p2) = ?
Since momentum is a vector quantity, we need to consider both the magnitude and direction. In this case, the orange ball continues in the same direction after the collision, so the magnitude of its momentum decreases from 135 g · m/s to 60 g · m/s.
Using the principle of conservation of momentum:
p1 + 0 = p1' + p2
Substituting the given values:
135 g · m/s + 0 = 60 g · m/s + p2
Simplifying the equation:
p2 = 135 g · m/s - 60 g · m/s
p2 = 75 g · m/s
Now, we need to convert the momentum of the green ball from grams to kilograms:
1 g = 0.001 kg
p2 = 75 g · m/s * 0.001 kg/g
p2 = 0.075 kg · m/s
Therefore, the momentum of the green ball right after the collision is 0.075 kg · m/s.