A balanced lever has two weights on it, the first with mass 5 kg 5kg and the second with mass 80 kg80kg. If the first weight is 16 m16m from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
May 8, 2018

The second mass is 1m1m 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=FxxrM=F×r), we can write an equation for the balance:

F_1xxr_1=F_2xxr_2F1×r1=F2×r2

Now, lets plug in our numbers:

F_1=5kgxxgF1=5kg×g
F_2=80kgxxgF2=80kg×g
r_1=16mr1=16m
r_2=Xmr2=Xm

I multiplied the masses by the gravitational constant gg 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)