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

Answer:

#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 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#