A toy car rolling down a loop-the-loop track demonstrates the minimum height it must start at to successfully negotiate the loop.
What it shows:
For an object to move in a vertical circle, its velocity must exceed a critical value vc=(Rg)1/2, where R is the radius of the circle and g the acceleration due to gravity. This ensures that, at the top of the loop, the centripetal force balances the body's weight. This can be shown using a toy car on a looped track.
How it works:
The car is released from the top of a ramp and runs down a slope towards the loop (figure 1). The velocity with which the car tackles the loop is dependent upon its initial height h, i.e. its initial potential energy. Should the gained kinetic energy be too small so that the car is traveling at below its critical velocity, it will leave the track and follow a parabolic path for part of the loop. Neglecting friction, critical velocity at the top of the loop is attained for a release height h=(2.5)R.
figure 1. car looping-the loop
Setting it up:
Best mounted on top of the lecture bench, with a clamp stand holding the starting ramp. Provide a soft cushion at the end of the track to prevent the car diving spectacularly off the end of the bench.
These type of tracks are made by a couple of manufacturers, such as Hot Wheels™ by Mattel® at greater cost than when I got one for Christmas. Although the cars themselves have very good bearings and little frictional losses, the losses nevertheless require a starting height greater than (2.5)R. If more quantitative results are desired, use the previous demonstration, Crashing Pendulum, which does not suffer from frictional losses.