The fact that same magnetic poles repel each other is the base for design of many industrial equipments. Repelling magnets are often part of another electrical or mechanical system. When you attempt to move the North pole of one magnet toward the North pole of another magnet, initially the other magnet may be pushed away, but soon it flips over and the South pole of that face and attract your magnet.
Many studies have been done on levitating objects with magnetic force, however it is now proven that 100% levitation for a non moving object is impossible. Partial levitation is now used in construction of high speed magnetic trains. Many other instruments and equipment also use repelling properties of magnets.
Following are some of the projects that can be made using magnets with same poles facing each other. They are all applications of magnet levitation.
In this project you will make a set of magnet rings to float above each other while their balance is maintained using a wood dowel. You will then examine the flexibility of the floating rings and propose uses for such a floating set of rings.
You will need a base board, a 6" wood dowel or pencil and six ring ceramic magnets, make sure that the wood dowel or pencil fits the hole in the center of magnets. Also try to get painted magnets. A layer of paint will protect ceramic magnets from chipping.
Mount the pencil or wood dowel vertically in the center of the base board. If you use glue, you will need to wait a few hours until the glue is fully dry. Place the first ring magnet over the wood dowel and let it go down. Get a second magnet and bring it close to the first magnet to feel the magnetic forces and find out which two poles repel each other. Then insert this magnet in a way that when it gets to the first magnet, same poles are faced each other and two magnets will repel. So the second magnet will float.
This is a good science project for ages 6 to 13.