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?

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Answer 1 · 2016-01-03T11:06:08

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

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

Tony B 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 $x= 6m$

A balanced lever has two weights on it, the first with mass 42 kg 42 kg and the second with mass 14 kg14 kg. If the first weight is 2 m 2 m from the fulcrum, how far is the second weight from the fulcrum?