# Loop-the-loop

#### Abstract

A ball rolls down an incline and around a vertical circle only if it starts with at least a minimum height.

Yes

#### Principles Illustrated

There is a well defined minimum height for a sliding object or a rolling ball to complete the loop without falling off the track.

PHYS 3.4

#### Instructions

The minimum height required for a ball rolling around the loop can be calculated as part of a class exercise. We often use clickers to lead the students through the steps in the calculation. The results are then tested.

As an interesting twist, we find that the calculated minimum height is roughly right (a bit too low) if we use a ball from an old mouse. But the steel ball that came with the commercial apparatus needs a far greater initial height. This is – counterintuitively – because the steel ball does not have enough friction! The mouse ball rolls without slipping and thus dissipates relatively little energy, but the steel ball slides and loses mechanical energy rapidly. This can be seen easily if the balls are released from perhaps the midpoint of the loop. The mouse ball returns to nearly the same height, but the steel ball does not.

#### Safety

Individual teachers are responsible for safety in their own classes. Even familiar demonstrations should be practised and safety-checked by individual teachers before they are used in a classroom.