Topics: Mechanics - Conservation of Energy, Kinetic/Potential Energy, Static Friction
Equipment: Brass track, white cue ball.
Setup: Place the cue ball anywhere on the brass track. The farther from the center it is placed, the longer it will oscillate back and forth.
At the highest point of the track, when it is first placed, the ball has the greatest possible potential energy because of its height: U=mgh. However, its kinetic energy is zero because it is not moving yet: T=(1/2)mv2. Of course, the total energy E=T+U. When the ball is released and starts to pick up speed, it will eventually reach its lowest possible point, and therefore lowest potential energy. Neglecting resistive forces, energy is conserved and E remains the same, in which case U is now zero (arbitrarily), so T must be at its maximum value and therefore the ball is moving at maximum speed.
If we do not neglect resistive forces, we understand that there is a net loss of energy due to air resistance and friction from surface contact. This energy is not “destroyed” but dissipated in the form of heat (thermal energy). Still, the analysis changes only slightly. At this scale, just a small amount of energy is lost with each oscillation, so the discussion above remains mostly the same. The ball will not roll back and forth indefinitely, but instead the maximum height the ball reaches will decrease slightly with each oscillation. However, for demonstration purposes, the first several oscillations can assume the ideal case described above.
Location: Shelf B-g6
Keywords: Energy, Roll, Ball, Friction, Gravity