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

1 Answer
Jan 3, 2016

color(blue)(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.")

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

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

14 kg xx xm=14x kgm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equating LHS to RHS for equilibrium gives:

42 kg xx 2m = 14 kg xx xm

=> 84 kgm = 14x kgm

Remember that the units for x is m

Divide both sides by 14 kg (leaves x m on the RHS)

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

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

So x= 6m