Pool table

Abstract

This article explains a novel way of demonstrating the principle of conservation of energy. This can be difficult to demonstrate in the laboratory, but if students have been convinced of the conservation of momentum, twodimensional collisions on a pool table may be used.

Collision of a ball with a barbell and related impulse problems

“…Since the bodies are rigid, there is a constraining relation between these velocities for each body υ = V − ω × R (11) both initially and finally, where R is the position of the CM relative to the impact point on each object. Equation (11) specifies the initial values of υ 1 and υ 2 , plus four expressions for υ 1fx , υ 1fy , υ 2fx and υ 2fy .…”

“…(The more general problem of rough, unequal-mass discs has also been investigated theoretically and experimentally [10].) The impact is necessarily central, so if neither sphere is initially rotating then neither will be afterward, and equation (11) then implies that υ = V for each sphere both initially and finally. In that case, equations ( 12) and ( 3) can be simultaneously solved to obtain…”

“…For example, if sphere 2 is initially at rest and the collision is elastic then V 1fx = 0 and V 2fx = V 1ix . If the collision is on centre ('direct') that means the two spheres exchange their velocities; on the other hand, if the impact is oblique (i.e., the impact parameter b = (R 1 + R 2 ) sin θ is nonzero, where θ is the angle between υ 1i and the line of impact) then V 1f is in the y direction and V 2f is in the x direction, perpendicular to each other [11].…”