What is the final velocity of the combined mass system when billiard ball a, moving at speed 70.9 m/s, collides and sticks with billiard ball b, having the same mass and initially stationary?
The final velocity of the combined mass system is 35.45 m/s.
Principle of Conservation of Momentum
Momentum Before Collision:
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision. In this case, we have two billiard balls, with ball a moving at 70.9 m/s and ball b initially stationary. Since both balls have the same mass, their momenta before the collision can be calculated using the equation momentum = mass × velocity.
Momentum of Ball a:
Momentum of ball a = mass × velocity = mass × 70.9 m/s.
Momentum of Ball b:
Since ball b is initially stationary, its momentum is zero.
Combined Mass System After Collision:
After the collision, the two balls stick together and move as a combined mass system. Let's denote the final velocity of the combined system as v. According to conservation of momentum, the total momentum before the collision (momentum of ball a) is equal to the total momentum after the collision (momentum of the combined mass system).
Equation Setup:
(mass × 70.9 m/s) = (2 × mass × v) (since we have the combined mass system after sticking together).
Solving for Final Velocity:
Simplifying the equation, we find:
70.9 m/s = 2v
Dividing both sides by 2, we get:
v = 35.45 m/s
Therefore, the final velocity of the combined mass system is 35.45 m/s.