Lifting Board: Example

If you have to lift a 50 lb, 10 foot board, common sense prompts you to pick up the long board at its center because it balances more easily and is more easily handled.

Some of the physical ideas behind this common sense are that the weight effectively acts at the center of mass, and you don't have to exert extra torques to keep the board in equilibrium. If it is supported at the center, the weight of the board has a zero lever arm with respect to the point of support.

If you were able to lift the board by it's end, with your fingers extending 6 inches under the board, how much force would you have to exert?

Balance

Balance is a concept which implies equilibrium of torques. If you are dealing with a single object, the concept of balance implies that an object is supported in such a way that its weight does not produce any torque about the point of support. Since the weight can be considered to be concentrated at the center of mass for purposes of calculating torque, it follows that in order to have zero torque, the weight must have zero lever arm and that happens only if it is in line with the point of support (directly above or directly below).

Common sense tells you to pick up a long board under its center to balance it. What happens if you try to pick it up by one end?

Lifting a board by its end

If you were able to lift the board by it's end, with your fingers extending 6 inches under the board, how much force would you have to exert?

A force of 500 pounds to lift a 50 pound board??

But your thumb would get off more easily. It would only have to exert 450 lb.

Another way of stating why it is unreasonable to lift boards like this is to say that the board has a large mechanical advantage over your hand in terms of torque.

Lifting a board by its end

You don't lift boards by their ends because the board has a long lever arm and your fingers have a short lever arm. In this example, the board is said to have a mechanical advantage of 10 because its lever arm is 10 times longer. Since the torques must be equal for equilibrium, you have to exert a force 10 times as large.