A balanced lever has two weights on it, the first with mass #34 kg # and the second with mass #68 kg#. If the first weight is # 3 m# from the fulcrum, how far is the second weight from the fulcrum?

Question

A balanced lever has two weights on it, the first with mass #34 kg # and the second with mass #68 kg#.  If the first weight is # 3 m# from the fulcrum, how far is the second weight from the fulcrum?

Sebastian Acosta · Accepted Answer

The second weight #68kg# is #1.5m# from the fulcrum.

The balanced lever is a simple scale in this configuration. If the two weights balance each other then the distance from the fulcrum to each must be in proportion to the two weights. That is: #w_1*d_1=w_2.d_2# We were told that: #w_1=34kg; w_2=68kg; d_1=3m# So: #34kg*3m=68kg*d_2# #cancel(34kg)*3m=cancel(68kg)*d_2# #2d_2=3m# #d_2=1.5m#

Julia Aguilar · Answer

undefined To find the distance of the second weight from the fulcrum, use the formula for a balanced lever:

(mass of first weight × distance of first weight from fulcrum) = (mass of second weight × distance of second weight from fulcrum)

(34 kg × 3 m) = (68 kg × distance of second weight from fulcrum)

102 kg·m = 68 kg × distance of second weight from fulcrum

distance of second weight from fulcrum = 102 kg·m / 68 kg

distance of second weight from fulcrum = 1.5 m