What is the final speed of the 15 stationary balls in a game of pool?
The final speed of the 15 balls in a game of pool can be determined by applying the principle of conservation of linear momentum. The final speed is calculated as the ratio of the inertia of the cue ball to the total mass of the 15 balls.
Understanding Linear Momentum in Pool Physics
Linear Momentum: In physics, linear momentum is the product of an object's mass and its velocity. It is a vector quantity that represents the motion of an object along a straight line.
Conservation of Linear Momentum
Principle: According to the principle of conservation of linear momentum, the total momentum of a system remains constant if no external forces are acting on it. This means that the initial momentum of an object before a collision is equal to the final momentum after the collision.
Calculating the Final Speed
Formula: The final speed of the 15 stationary balls can be determined using the formula:
J = ΔP
m1u1 - m1v1 = 15m0v0
Where:
J is the inertia
m1 is the mass of the cue ball
u1 is the initial velocity of the cue ball
v1 is the final velocity of the cue ball
m0 is the mass of the 15 balls
v0 is the final speed of the 15 balls
By rearranging the equation, we can calculate the final speed of the 15 balls in terms of the inertia of the cue ball and the total mass of the 15 balls.
Final Calculation: v0 = -m / 15m0
Therefore, the final speed of the 15 stationary balls in a game of pool is determined as the ratio of the inertia of the cue ball to the total mass of the 15 balls.