8-Ball Pool Glancing Collision
Unit: Linear Momentum
Prerequisites
Later Topics
Multi-Step Problem Preview
Part 1 of 6 — sign up to solve the full problem!
Part 1
A cue ball (Ball A) of mass is moving across a frictionless pool table with an initial velocity in the direction. It strikes a stationary 8-ball (Ball B) of identical mass in a glancing collision. The collision is perfectly elastic.
Which of the following correctly identifies the conserved quantities for the two-ball system immediately before and after the collision?
Correct!
For the system consisting of the cue ball (Ball A) and the 8-ball (Ball B), we analyze the external forces. Since the pool table is frictionless, there are no external dissipative forces like friction acting on the system in the horizontal plane. The vertical forces (gravity and normal force) balance each other. Therefore, the net external force on the system is zero. According to the conservation of momentum principle:
Thus, total linear momentum is conserved.
The problem explicitly states that the collision is perfectly elastic. By definition, an elastic collision is one where the internal non-conservative work is zero, meaning the total kinetic energy of the system is conserved:
Therefore, both momentum and kinetic energy are conserved.
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