Equivalent force systems (statics)

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Homework Help Overview

The discussion revolves around the concept of equivalent force systems in statics, focusing on how to determine if different force systems yield the same resultant force and moments.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the criteria for equivalence between force systems and expresses confusion about reducing systems to a single force. They question the comparison between systems (a) and (b) and explore the moments calculated for each system.

Discussion Status

Participants are actively discussing the criteria for equivalent force systems, with some guidance provided regarding the need to compare resultant forces and moments. The original poster has received a response that affirms their observations about systems (a) and (b) not being equivalent, prompting further exploration of system (c).

Contextual Notes

There is a lack of visual context due to missing figures, which may impact the clarity of the discussion regarding the force systems in question.

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Homework Statement


See figure


Homework Equations


\sum F_{x} = 0

\sum F_{y} = 0


The Attempt at a Solution



I'm confused as to how to check which systems are equivalent.

Do I just have to simply reduce all the systems to one force?

I tried comparing systems (a) and (b) and they don't seem to be the same.

If I take moments about the bottom left corner,

M_{a} = 63N.m
M_{b} = 35N.m

I'm confused as to which route I should take to solve the problem. Any ideas?
 

Attachments

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Last edited:
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PhanthomJay said:
No figure attached.

Sorry about that, it should be in the OP now.
 
The force systems are equivalent if the resultant force and moments about a point, of each system, are the same. You are correct that 'a' and 'b' are not equivalent. What about 'a' and 'c'?
 
That's all I needed!

Thank you!
 

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