There's been all sorts of coil guns and rail guns being posted... but here's an interesting alternative. Not really useful, but amusing and effictive as a physics demo. The concept? Conservation of momentum
You'll need some magnets -preferably of the same size, type and somewhat strong (weak magnets do not work as effectivly). You're also going to need some ball bearings that show visible reactions in magnetic fields (aka nickel, coblat and iron/ferrous steel).
You're also going to need a ruler or some sort of straight edge. Movie on next step ;)
Step 1: Setup and Demonstration
I'm using the magnets found inside the magnetix brand of magnetic toy.
Place one magnet on one ball - then place the ball on your straight edge. Attach to the ball (but not to the magnet), one or two additional balls. You can stop here - or repeat this as many times as you want/can.
Take a different ball - and roll it towards the magnet on the first collection of magnet/balls. You should notice that once the ball is inside the magnetic field, it accelerates towards the magnet and makes contact with the magnet/ball cluster. Once contact is made, the last ball(s) separate in the same direction as the original ball.
This phenomina demonstrates the concept of conservation of momentum. If you were to repeat this demonstration without the magnets, you will have the same results with less motion.
The rest of this instructable has more information/examples for those that want to know more.
Step 2: Giant Clusters - Efficiency
This setup demonstrates what happens when the force of impact is great enough to separate more than one ball.
1st Cluster: Two magnets with four balls
2nd Cluster: Two magnets with five balls
Gently roll the ball into the first cluster. Depending on how much energy you give the first ball (how fast you push it), an additional ball me separate from the first cluster (see second picture). why? The momentum collected just before the initial impact overcame the force required to separate one ball and also the second ball. Ideally, you want all of this momentum going into the first ball rather than the available momentum being split between two different balls.
Going further -- increasing efficiency.
Now, remove one ball from the first cluster. But leave the second cluster alone. (See third picture) Repeat the experiment.
Notice in the fourth picture (after impact), that the first cluster remained intact but the second cluster is missing two balls! why? Because more momentum was put into the ball ejected off the first cluster (simply by removing one ball from the system), the momentum going into the second cluster was great enough to remove two balls.
why do the balls stick together in the first place? In case someone needs to ask. This is due to the magnetic force between the balls and magnet. Even the final ball has a magnetic force on it, but that force is weaker compared to each ball closer to the magnet. To proove this - make the first cluster made up of one ball. Now, gently push another ball into it. The ball/magnet system will not separate because the force between the magnet and ball is too great.
Step 3: Ramps!
What happens when we go up a ramp?
To demonstrate a special case, I setup this demo to show what happens at a sort of "critical point."
From the first image, you can see that the second cluster is quite large -- and there are balls on either side of the magnet. We will gently push a ball into the first cluster and see what happens.
In the middle of the action (picture 2). Notice how the last ball in cluster two is blurry -- it is currently in motion - going up the ramp.
Aftermath (picture 3). What happened? It looks like we ended just where we started?
Why? As the ball on the end of cluster 2 goes up the ramp, it is gaining potential energy as a result of gaining height. Once it reaches its apex, it will return down the ramp and impact with cluster 2. The imparted momentum is great enough to release the ball on the opposite end of the cluster resulting in picture 3.