On the other hand you need to take account of the energy of the sphere rolling which is stated explicitly.
Marble loop the loop physics.
Chris got asked how fast you would need to be going to complete a loop the loop this is what we got.
The loop is tricky.
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.
A loop the loop track consists of an incline that leads into a circular loop of radius r.
First we need to find the minimum speed required at the top of the loop.
I solve the loop the loop first year undergraduate and ap physics problems.
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.
Build a miniature roller coaster and see if you can get marbles to go the distance and upside down.
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.
Loop the loop with a little physics.
It takes extra energy for the marble to stay on the track so it has to slow down when it goes through the loop.
We are going to find the minimum speed you require to complete the loop we ll do this via an energy argument.
When the marble finally gets to the floor it has all kinetic energy and no potential energy.
Your expression for the velocity looks right.
When you let go of the marble its potential energy is converted into kinetic energy the energy of motion.