Central Forces 2023
Consider an air hockey puck of mass \(m\)
tethered to a peg in the middle of an air hockey table.
The tether is made from a small piece of thread of length \(L\). You give the
puck a push so that its initial
angular momentum is \(\ell\),
Briefly explain why this is a central force system.
A central force problem involves two objects. Find an approximate formula for the reduced mass of this central force system and explain briefly, in words, why this makes sense.
Make a sketch of the potential energy of this system plotted vs. \(r\), the distance from the peg.
Recall that the effective potential is the SUM of the potential (the one you just plotted!!!) and the kinetic energy due to the angular part of the motion.
\[U_{\text{eff}}=U(r)+\frac{\ell^2}{2\mu r^2}\]
Make a sketch of the effective potential.
Briefly discuss the possible orbit shapes that can arise from this effective potential.
How should you push the puck to establish a circular orbit?
(i.e. give the initial position and direction of push).
