Forces moving forces

The idea of work done can be extremely useful when designing machines that make life easier and sometimes even enable us to do things that are “impossible”. For example, it is fair to say that most humans are not capable of lifting masses of a tonne (1000 kg) or more. And yet that is indeed possible without using any powered machinery – provided that you know how to apply the principle of “work done”.

To understand this, we first need to realise that if we wanted to lift 1000 kg up a height of 10 m then that would require the transfer of at least 10 000 J. We get this figure from the equation for work done, which states;

work done = force x distance (moved in the direction of the force)

Remember that we must use SI units for this equation to work; force must be in newtons (N) and distance must be in metres (m) to give work done in joules (J).

Obviously, I hope, we could achieve the transfer of 10 000 J in an infinite number of different ways, including;

• raise a mass of 1000 kg through a height of 10 m (the example above)
• raise a mass of 100 kg through 100 m
• raise a mass of 500 kg through 20 m
• raise a mass of 10 000 kg through 1 m

In each case above, using the work done equation (the product of the force and the distance) gives exactly the same answer, 10 000 J.

Now here comes the clever bit…

We know, from the conservation of energy, that if we put a certain amount of energy into a system then, assuming that there is no waste energy, we can get the same energy out in a different form.

in other words, if we could carry a 10 kg mass (easy) up a height of 1000 m (equivalent to climbing up a small mountain, such as Mount Snowdon in Wales, which can easily done in a day just by walking up the path provided) then we have transferred the same amount of energy as if we had lifted a one tonne mass from the ground onto the roof of a typical house!

You may rightly say that these aren’t really the same thing and it’s only the calculations that give the same answers, which is mathematics rather than physics. But suppose we had a machine that could transfer the energy from one situation to another automatically. So as you walk up the mountain carrying the 10 kg mass, that same energy is transferred (imagine it being teleported) to a one tonne mass that is very slowly being raised off the ground. By the time you reached the top of the mountain with your 10 kg mass, the 1000 kg mass would have been raised to the top of the house!

This is exactly how simple machines, such as levers, gears, and pulleys work. In all cases, the machines offer different combinations of force and distance to make it possible to move a large force through a small distance by applying a smaller force that is moved through a larger distance. Make sure that you are clear about this trade-off because it is the key to understanding levers and gears (which you need to know about) as well as hydraulic systems, which we will meet later.

So to summarise… assuming that we have the right values, moving a large force through a small distance can involve the same energy transfer as moving a small force through a large distance

large force x small distance = small force x large distance

To understand this in a common real-world situation, read this follow-up post about levers and gears.

If you want to go back and remind yourself about the connection between work done and the equation for gravitational potential energy, then you can do that here.