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Multiplying Force

If a person, such as Mendel, uses a lever to move a heavy box, he is taking advantage of a principle known as multiplying force. On his own he could not generate enough muscular effort to move a 300 kilogram packing case, but he could do the job using an iron bar as a lever and adjusting the fulcrum of the lever so it was closer to the box than it was to him.

It was the Greek mathematician (who lived in the years 287 - 212 BC) explained this principle scientifically. He saw that the lever was a simple machine which transfered a force from one point to another. However, the principles of this leverage could be adjusted in such a way so that the force was multipled.

Mendel could move a packing case across a room using this principle. A metal bar, the lever, is 2.1 meters long. With this bar he could apply a force of 15 kilograms. If the fulcrum of the lever is placed just 0.1 meters from the box to be moved, we can do the calculations this way:

Torque generated by Mendel on his end of the lever is:
f x d
(which in this case is 15 x 2 = 30 units)

Torque generated at the box is:
f x d
(which in this case is 300 x 0.1 = 30 units)

The torques are the same at each end of the lever, but how far will the box move?

Not far. Look at the diagram . Mendel has to move his end of the lever much further than the box moves at the opposite end. Never the less, the box does move, and so by repeated applications a monk like Mendel with minimal force, can move around a heavy object using the lever, and the 'multiplying' effect of the forces used.

However, and it is a big 'however', Mendel is not getting 'something for nothing'. The product of the force multiplied by the distance still remains the same at both ends of the lever. This property is called work and is usually written in scientific equations using the letter w.

Work is done when a force moves an object through a distance.

w = f x d

The units of work are called joules after the English physicist, or ergs, depending on which units of measurement are used.

Science@a Distance
© 2001, Professor John Blamire