Proof of equilibrium equations?

[bhsmith]

proof of equilibrium equations??

Homework Statement

I have a statics test tomorrow, and I have to give a proof type answer of how the equilibrium equations (sum of forces and sum of moment are zero) are derived.

Homework Equations

The Attempt at a Solution

I'm not sure how to do this, I understand that

because the system is in equilibrium then the acceleration is zero and Force=mass(aceleration) which would imply that mass is zero. But I don't think I'm going about that the right way.

As for the moment, I'm not sure what to do.

The way he did it in class was using Newtons first and third laws to prove it, but I didn't quite understand how he went about it.

Thanks for any help!

 

[rock.freak667]

I would have thought it would have been a simple case of Newton's 2^nd Law where ∑F_n = ma_n (acceleration in the 'n' direction) and in equilibrium, a_n = 0 m/s².

 

[bhsmith]

Ok, Maybe I will look into that more. I wasn't sure if i was going down the right path with that thought.
But do you have any thoughts on the moment?

 

[rock.freak667]

Ok, Maybe I will look into that more. I wasn't sure if i was going down the right path with that thought.
But do you have any thoughts on the moment?

Well for Newton's 1^st Law to apply, you'd need to know the resultant force on the body is zero for it to be at rest or in motion (in equilibrium, so you know a = 0)

For Newton's 3^rd Law - You'd pretty much use this to get the sum of forces, for example reaction forces.