Energy and the "Air Ball"
In the activity "Air Ball" a spring is used to throw a group of magnets in a reproducible way. The spring is just a piece of plastic that can be bent. It takes a force to bend the spring, which increases with larger deflection. Since both a force and a distance are involved, we are transferring energy to the spring. The energy that is stored in the spring can be called elastic energy. Provided that the spring is always deflected the same amount, the amount of stored energy is the same. When the spring is released, this energy is converted into other forms -- the motion of the spring and the magnets that is riding on it. The magnets and the spring are moving at the same speed, until the magnets are launched; since the magnets weigh more than the moving part of the spring, they get a large share of this energy as they are thrown into the air.
Initially the launched magnets have kinetic energy, but as they move upwards, this is converted into gravitational energy. At the highest point all of the kinetic energy has been converted, and we have the relationship
Energy given to the magnets = increase in gravitational energy = (weight of the magnets) x height
If we assume that all of the energy of the spring is given to the magnets, then the product weight x height will be the same for any number of magnets. Thus one magnet will go higher than several stuck together. In the activity it was found that while one magnet definitely goes higher than two, it wasn't twice as high -- it didn't get quite as much energy as a group. This is because the single magnet is moving faster when it leaves the spring board. The spring board is moving with the magnet up to that point, and thus with a single magnet, the spring board has a little more kinetic energy. The springboard steals a share of the energy, corresponding to its mass. Because the spring board has a very small mass, the effect is small, but detectible.
The energy stored in the spring can be estimated by Force x Distance where Distance is the displacement of the spring and Force is the force needed to do this. Then if it takes 4 N to displace the spring 0.0125 m, we have
Energy = 4 N x 0.0125m = 0.05 J
-- enough to lift a 4 magnets (0.28 N) to a height of 0.18 m. This is quite consistent with what we observe.
The energy concept puts a limit on how high a thrown magnet can go, but doesn't explain what happens in detail. In fact, the energy description seems to imply that after the magnet reaches the highest point it could just stay there. After all, the speed is zero! However, the Law of Force and Acceleration does not permit this. The magnet is always subject to the gravitational force, and (ignoring the effect of the air) this is the only force acting. So there is an unbalanced force pulling down on the moving magnet at all times, causing it to accelerate downwards (in the direction of the force).
When the magnet returns to the height at which it left the spring, it has converted the potential energy back into kinetic energy. Its potential energy is the same as when it started on the way up, and thus so is the kinetic energy. The magnet is coming down just as fast as it was going up initially.