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