Chris got asked how fast you would need to be going to complete a loop the loop this is what we got.
Marble loop the loop physics.
Build a miniature roller coaster and see if you can get marbles to go the distance and upside down.
Your expression for the velocity looks right.
It takes extra energy for the marble to stay on the track so it has to slow down when it goes through the loop.
Abstract this is a really fun project even if you don t like going on roller coasters yourself.
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.
For ease we ll ignore friction.
On the other hand you need to take account of the energy of the sphere rolling which is stated explicitly.
But we have to get a few other things taken care of.
When the marble finally gets to the floor it has all kinetic energy and no potential energy.
Loop the loop with a little physics.
First we need to know the minimum speed at the top of the loop for the mass to remain on the track.
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.
I solve the loop the loop first year undergraduate and ap physics problems.
When you let go of the marble its potential energy is converted into kinetic energy the energy of motion.
We are going to find the minimum speed you require to complete the loop we ll do this via an energy argument.
The loop is tricky.