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 # 4 m# from the fulcrum, how far is the second weight from the fulcrum?

#color(blue)("Comment")#
As we are determining the distance it does not matter what units of weight we use as long as they are consistent.

I am also going to demonstrate how to deal with the units of measurement. If you deal with 'Statics' to any extent then manipulating units is exceptionally important!

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If the moments do not match then it means that the system is in motion. We can use this fact to determine the moment arms needed to establish equilibrium.

A Moment is the number resulting from an applied force multiplied by its distance to a point of rotation ( actual or theoretical).
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#color(blue)("Taking Moments about the fulcrum B")#

Let clockwise moment be positive.
Let anticlockwise moments be negative

Then for equilibrium to exist

#(+(6xx4) Kgm) +(-(7xx x) Kgm)=0#

#color(brown)(":::::::::::: Units are very important:::::::::::::::")#

#color(brown)("Note that weight"xx"distance"->Kgxxm->Kgm#

#color(brown)( "::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::")#

For this to be true then:

#24 Kgm=7x Kgm#

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#color(blue)("To find the value of "x)#

To find #x# divide both sides by #7Kg#: Note I have included the units

#24/7color(white)(.) (cancel(Kg)m)/cancel(Kg) = (cancel(7Kg))/(cancel(7Kg))xx xm#

#x ~~3.429 metres# to 3 decimal places