Question

A balanced lever has two weights on it, the first with mass `5 kg` and the second with mass `80 kg`. If the first weight is `16 m` from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

The second mass is `1m` from the fulcrum

Explanation:

Balancing a lever means balancing the moment or torque in the system.

Knowing that moment is equal to the force applied multiplied by the length of the lever arm (`M=Fxxr`), we can write an equation for the balance:

`F_1xxr_1=F_2xxr_2`

Now, lets plug in our numbers:

`F_1=5kgxxg`
`F_2=80kgxxg`
`r_1=16m`
`r_2=Xm`

I multiplied the masses by the gravitational constant `g` to assure that it's a force. This is an extra step for this specific question, but important when dealing with units.

`cancel(g)xx5xx16=cancel(g)xx80xxX`

Notice that the gravitational constant cancels (why I said this was extra for this question)

`5xx16=80X`

`80=80X`

`color(green)(rArrX=1m)`