Question

A balanced lever has two weights on it, one with mass `1` `kg` and one with mass `8` `kg`. If the first weight is `9` `m` from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

The `8` `kg` mass will be `1.125` `m` from the fulcrum in order to balance a `1` `kg` mass placed `9` `m` from the fulcrum.

Explanation:

For the lever to be balanced, the torque on each side of the fulcrum must be balanced.

The torque due to the first weight is given by `\tau = Fr = mgr` where `r` is the distance from the fulcrum, since the weight force on the mass is given by `F=mg`.

`\tau = Fr = mgr = 1xx 9.8xx9 = 88.2` `Nm`

The torque due to the second mass must have the same value:

`\tau = mgr`

Rearranging to make `r` the subject:

`r = \tau/(mg) = 88.2/(8xx9.8) = 1.125` `m`

This is as we would expect: a larger mass needs to be closer to the fulcrum to balance a smaller mass further from the fulcrum.