# 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?

May 8, 2018

The second mass is $1 m$ 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 ($M = F \times r$), we can write an equation for the balance:

${F}_{1} \times {r}_{1} = {F}_{2} \times {r}_{2}$

Now, lets plug in our numbers:

${F}_{1} = 5 k g \times g$
${F}_{2} = 80 k g \times g$
${r}_{1} = 16 m$
${r}_{2} = X m$

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.

$\cancel{g} \times 5 \times 16 = \cancel{g} \times 80 \times X$

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

$5 \times 16 = 80 X$

$80 = 80 X$

$\textcolor{g r e e n}{\Rightarrow X = 1 m}$