A balanced lever has two weights on it, the first with mass 42 kg 42kg and the second with mass 14 kg14kg. If the first weight is 2 m2m from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
Jan 3, 2016

color(blue)(x= 6m)x=6m

Did you know you can treat units of measurement the same way as numbers? I have shown this in my solution.

Explanation:

Tony BTony B

For the system to be in equilibrium (not rotating or moving in any way) all the 'moments' have to cancel each other out.

color(blue)("Taking moment about the fulcrum.")Taking moment about the fulcrum.

color(brown)("Consider the LHS of the fulcrum")Consider the LHS of the fulcrum

42 kg xx 2m = 84 kgm -> "force "xx" distance")42kg×2m=84kgmforce × distance)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(brown)("Consider the RHS of the fulcrum")Consider the RHS of the fulcrum

14 kg xx xm=14x kgm14kg×xm=14xkgm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equating LHS to RHS for equilibrium gives:

42 kg xx 2m = 14 kg xx xm42kg×2m=14kg×xm

=> 84 kgm = 14x kgm84kgm=14xkgm

Remember that the units for xx is m

Divide both sides by 14 kg14kg (leaves x mxm on the RHS)

=> 84/14 (kgm)/(kg)= xcolor(white)(.)m8414kgmkg=x.m

6 color(white)(.)(cancel(kg)m)/(cancel(kg)) =xcolor(white)(.)m

So x= 6m