[kristo]

On one end of a 6m bar there is a 600kg weight, on the other end there's a 200kg weight, the bar itself weighs 20kg.
Where shall the point of support be so that the bar is balanced?

I hope you understand it, English isn't my first language.. :(

[Capuchin]

Hi, here you need to balance the moments being supplied by each weight.

So if we define x as the distance from the 600kg weight to the support

Using:
Moment = Force * Perpendicular distance (from fulcrum)
and:
Counterclockwise moment = Clockwise moment
we find:



this describes the moment felt in the clockwise and anticlockwise direction.
600*x is the moment from the weight
20(x/6) is the weight of the bar felt in this direction
x/2 is the distance that the weight of the bar acts from the fulcrum

then the same is written for the other direction

The first step is obviously to cancel g, this is why I put it in brackets.

You can solve this equation for x to find the distance that the fulcrum must be from the 600kg weight

If you have any problem with understanding, please ask further!
good luck!

PS: i did this very quickly and have tried to catch any errors, I make no claims to correctness and you should check everything yourself.

[kristo]

Thanks a lot for your help!
I get this far, but don't really know what to do next, a little help, please?

[Capuchin]

Expand the brackets, group like terms, solve the quadratic, that's about all there is to it.

Hopefully you get a meaningful answer! :D

[kristo]

So, x is about 1.5 meters, right?

[Capuchin]

No idea but that sounds about right! :)
if the bar was weightless then it would be exactly 1.5, so nearly 1.5 taking into account the weight of the bar sounds spot on.
Make sure you understand how I made the equation in my first post, that's the most important thing to learn.

[kristo]

I understand it for most of the part, but could you explain the x/2 and x/6 part a bit?

[Capuchin]

x/6 is the fraction of the bar that is on that side of the fulcrum, so by multiplying it by 20g we get the weight of the bar on that side of the fulcrum.

x/2 is the distance that this weight acts from the fulcrum. You understand that a solid object can be simplified to a point at the centre of mass of the object? Same principle here.

so by multiplying them we find the moment from the bar in the anticlockwise direction.

[kristo]

I think I got it now, thank you :).
Sorry about the half comment, accidentally pressed F5 while writing it and can't edit.

[Capuchin]

Heh no problem! Thanks for excercising my moment knowledge!