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

1 Answer
May 8, 2018

Answer:

The second mass is #1m# 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=Fxxr#), we can write an equation for the balance:

#F_1xxr_1=F_2xxr_2#

Now, lets plug in our numbers:

#F_1=5kgxxg#
#F_2=80kgxxg#
#r_1=16m#
#r_2=Xm#

I multiplied the masses by the gravitational constant #g# 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)#