Levers and Gears

We have covered the theory of work done so now it’s time to look at some simple machines that trade force against distance to make tasks easier than they would otherwise be.

In this post we will look at levers and gears, which “magnify” forces by moving a smaller force through a larger distance. This is sometimes known as “mechanical advantage” but the GCSE Physics course doesn’t use that term so you will only need it if you are doing further research online or in other textbooks.

Let’s start by looking at the key vocabulary that you need to know;

• A lever is a system of rotational forces that act about a pivot (the point of rotation).
• Levers do not go “up” and “down”: they rotate clockwise and anti-clockwise.
• The effect acting on a lever is called a moment.
• When a lever is balanced, the moments (clockwise and anti-clockwise) are equal.
• The lever equation is;

moment (Nm) = applied force (N) x perpendicular distance (m)

• A gear is a system of rotating cogs that act about two or more different axes.
• Cogs can be connected either by directly touching each other or via a chain.
• Cogs that touch each other always rotate in opposite directions.
• Smaller cogs rotate faster than bigger cogs in the same set of gears.
• The rate of rotation for a cog is inversely proportional to its number of teeth.

When you use an ideal lever, all of the energy that is input by the applied effort is transferred to the load to produce a greater force that moves through a smaller distance.

For example, suppose that you want to open a tin of paint that had its lid sealed in the factory using a force of 500 N. Most people can’t easily apply a force of 500 N (equivalent to lifting a mass of approximately 50 kg) so the usual way to open a paint tin is by inserting a flat-tip screwdriver into the gap between the tin and its lid, as shown below.

When used like this, the screwdriver is providing a lever action with the pivot point very close to the lid and the applied load pushing down on the screwdriver handle. A bird’s-eye view of the system, together with a simplified lever diagram, is shown below.

The force that had to be applied to the screwdriver to open this particular tin was about 10 N. This means the applied moment was approximately 1.85 Nm (remembering to convert 185 mm into 0.185 m).

When the lid first moved, the resistance moment was also equal to 1.85 Nm. By rearranging the moment equation we can calculate that the resistance force of the lid, acting over a distance of just 0.005 m, must have been 370 N. This is considerably more than the weight of a typical suitcase that is loaded into the hold of an aeroplane!

This magic is possible because the screwdriver had to be moved downwards by about 120 mm to make the lid lift by just 3 mm.

This is consistent with the conservation of energy and the work done equation (click here if you need to refresh your memory about “work done”).

The screwdriver had an applied force of about 10 N and moved through 0.12 m, resulting in the transfer of 1.2 J.

The lid had a resistance force of 370 N and moved through 0.003 m, equating to 1.1 J of energy.

In theory, the energy input (1.2 J) should be equal to the output energy (1.1 J) but this is a real life situation and some of the figures were estimates. In any case, some of the input energy will have been transferred by the screwdriver sliding over the pivot and generating a small amount of waste heat through friction.