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

Answer:

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.