But we have to get a few other things taken care of.
Marble loop the loop physics.
Abstract this is a really fun project even if you don t like going on roller coasters yourself.
Your expression for the velocity looks right.
We are going to find the minimum speed you require to complete the loop we ll do this via an energy argument.
First we need to know the minimum speed at the top of the loop for the mass to remain on the track.
It takes extra energy for the marble to stay on the track so it has to slow down when it goes through the loop.
Loop the loop with a little physics.
I solve the loop the loop first year undergraduate and ap physics problems.
A loop the loop track consists of an incline that leads into a circular loop of radius r.
On the other hand you need to take account of the energy of the sphere rolling which is stated explicitly.
The loop is tricky.
For ease we ll ignore friction.
When the marble finally gets to the floor it has all kinetic energy and no potential energy.
You ll build a roller coaster track for marbles using foam pipe insulation and masking tape and see how much of an initial drop is required to get the marble to loop the loop.
First the center of the marble doesn t move from 0 to 2r it moves from r to 2r r so the potential energy due to this is smaller than mg 2r which is what you had in your expression.
What is the minimum height that a mass can be released from rest and still make it around the loop without falling off.
Build a miniature roller coaster and see if you can get marbles to go the distance and upside down.