A balanced lever has two weights on it, one with mass 1 kg and one with mass 8 kg. If the first weight is 9 m from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
May 20, 2017

The 8 kg mass will be 1.125 m from the fulcrum in order to balance a 1 kg mass placed 9 m from the fulcrum.

Explanation:

For the lever to be balanced, the torque on each side of the fulcrum must be balanced.

The torque due to the first weight is given by \tau = Fr = mgr where r is the distance from the fulcrum, since the weight force on the mass is given by F=mg.

\tau = Fr = mgr = 1xx 9.8xx9 = 88.2 Nm

The torque due to the second mass must have the same value:

\tau = mgr

Rearranging to make r the subject:

r = \tau/(mg) = 88.2/(8xx9.8) = 1.125 m

This is as we would expect: a larger mass needs to be closer to the fulcrum to balance a smaller mass further from the fulcrum.