### Levers

It's all a matter of balance. A plank of wood placed across a log becomes a seesaw; a playground device known to children of all ages. The plank is rigid, stiff, and only in contact with the log at one point. It moves easily about this point and provides endless hours of fun as the users rock up and down sitting on the ends of the plank.

The seasaw is a good and simple example of a machine; any device that is capable of of moving a force from one point to another. The plank of wood is known as a lever and the log across which it rotates is called a fulcrum. In a well made seesaw the plank is balanced exactly over the log at its center of gravity, so that its ends neither tip one way or the other. The whole of the weight of the plank (lever) is concentrated in the center where it rests on the log. Everything is in balance, a situation called equilibrium.

Suppose a child climbs on one side of the seesaw. The weight of the child pushes down the plank on that side of the seesaw and the equilibrum is disturbed. Put in scientific language, the downward force (the weight of the child) applied to the end of the lever represents a torque, and the lever rotates around the fulcrum in the direction of the torque. The opposite end of the lever moves in the opposite direction.

A second child joins in the game and climbs on the other end of the seesaw. If the two children are the same weight then the seesaw moves and again comes into balance in about the same position. Now there are two opposite torques, or downward forces, opperating at opposite ends of the lever in opposite directions. The system has come into balance, or equilibrum once again.

One child begins to crawl along the plank towards the center and the log. Suddenly everything changes, the seesaw tips violently and the child that hasn't moved crashes to the ground. What happened? It is still the same seesaw and the same children. What is going on?

For a lever to be at equilibrium the torques, or forces pushing down on the opposite sides, must be equal, otherwise the lever moves. Assume that the lever is 4 meters in lenght, with 2 meters on each side of the fulcrum (log), and that each child weighs 60 kilograms. When the lever is at equilibrum, a downward force of 60 kilograms is being applied at a distance of 2 meters from the fulcrum on each side of the seesaw. The exact torque can be calculated by multiplying these two values, thus - force x distance, or f x d, which in this case is 60 x 2 = 120 units.

As one child moves towards the center of the seesaw, the torques change. On one side it stays at the 120 units, as calculated above, but on the other side, as the child moves in one meter, the new torque (f x d) becomes 60 x 1 = 60 units. This torque is less than that on the other side, the equilibrium is lost and so the lever moves and the seesaw rocks.

For the balance to be restored, another 60 kilogram child would have to be placed at the one meter distance. Now the torques would again balance, thus - (f x d), or (60 + 60) x 1 = 120 units. From this example, we get an important principle. The torque applied to a simple lever is the product of two things; the force applied and the distance from the fulcrum at which it is applied. This turns out to be a critical property.

Science@a Distance
© 2001, Professor John Blamire