Calculating unknown forces using the principle of moments.

[Craptola]

Hello, run into a bit of a stumbling block studying moments perhaps someone could nudge me in the right direction.

Homework Statement

A uniform metre ruler is balanced horizontally on a knife edge at its 350mm mark, by placing a 3.0N weight on the rule at its 10mm mark. Calculate the weight of the ruler.

Homework Equations

Not entirely certain but I have to assume it involves
Moments = force x perpendicular distance and the principle of moments.

The Attempt at a Solution

This is where I'm stuck I've reasoned (probably wrongly) that:

(3N x 0.34m) + (y x b) = (z x a)

and y + z = the weight of the ruler.

Where y is the weight of the 350mm long side of the ruler

b is the distance between where the force y is acting (which I'm assuming is just its midpoint) and the pivot

z is the weight of the 650mm side of the ruler.

a is the distance between where the force z is acting (which again I'm assuming is its midpoint) and the pivot.

Not only am I extremely doubtfull that my above formula is correct I can't really see any way that I can determine the weight of the ruler form the information I've been given.
Any help would be greatly appreciated.

 

[LawrenceC]

Where does the 650mm come from? It was not stated in the problem.

 

[Craptola]

The pivot is at the 350mm mark on the ruler which is 1m long, therefore there are 350mm of ruler before the pivot and 650mm after it.

 

[LawrenceC]

If I assume correctly that the total length of the ruler is 650mm, you should sum moments at the fulcrum and set their sum to zero. On one side you have the weight at a certain distance from fulcrum. You also have the ruler weight that would contain the unknown total weight applied to each side of the fulcrum. Since ruler is uniform and you know what proportion is on each side of the fulcrum, you can sum those moments as well. Don't forget the weight of each overhanging side is assumed concentrated at the center of mass which you know because you know where the fulcrum is positioned. The equation you wind up with has one unknown, the weight. Solve for it.

 

[LawrenceC]

Our posts overlapped. So the length is 1000mm. Same method applies. Sum moments at fulcrum and equate to zero. Only unknown is weight.