# A balanced lever has two weights on it, the first with mass 6 kg  and the second with mass 7 kg. If the first weight is  12 m from the fulcrum, how far is the second weight from the fulcrum?

Jan 9, 2017

#### Answer:

The 7 kg weight must be located at 10.3 m from the fulcrum.

#### Explanation:

To understand the balancing of a lever you must think in terms of the torque acting on each side of the fulcrum, because this is what actually is balanced.

To calculate torque, you multiply the amount of force acting on the side of the lever (the weight of the object) by the distance of that weight from the fulcrum (usually called the torque arm, $r$).

So, on one side we have 6 kg at 12 m

${T}_{1} = 6 k g \times 12 m = 72 N m$

The torque on side 2 must match this for a balance to exist

${T}_{2} = 72 N m = 7 k g \times r$

so, $r$ must equal $72 \div 7 = 10.3 m$