Question

A balanced lever has two weights on it, the first with mass `1 kg` and the second with mass `7 kg`. If the first weight is `8 m` from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

`~1.14` meters

Explanation:

When a lever is balanced, the torque exerted on either side of the fulcrum is equal, so the lever is held in equilibrium.

`tau = rFsintheta` where `tau` is the torque on one side of the lever and `theta` is the angle that the side makes with the fulcrum.

`tau_1 = (1*9.8) * 8 * 1`
`tau_2 = (7*9.8) * r * 1`

Knowing that `tau_1` and `tau_2` are equal, we can combine the two equations to solve for `r`.

`9.8 * 8 = 68.6r`
`78.4 = 68.6r`
`r = 1.14`