Abstract this is a really fun project even if you don t like going on roller coasters yourself.
Marble loop the loop physics.
When you let go of the marble its potential energy is converted into kinetic energy the energy of motion.
First we need to know the minimum speed at the top of the loop for the mass to remain on the track.
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.
I solve the loop the loop first year undergraduate and ap physics problems.
It takes extra energy for the marble to stay on the track so it has to slow down when it goes through the loop.
But we have to get a few other things taken care of.
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.
A loop the loop track consists of an incline that leads into a circular loop of radius r.
Loop the loop with a little physics.
Chris got asked how fast you would need to be going to complete a loop the loop this is what we got.
What is the minimum height that a mass can be released from rest and still make it around the loop without falling off.
For ease we ll ignore friction.
Build a miniature roller coaster and see if you can get marbles to go the distance and upside down.
The loop is tricky.
On the other hand you need to take account of the energy of the sphere rolling which is stated explicitly.
When the marble finally gets to the floor it has all kinetic energy and no potential energy.