Equivalent force systems (statics)

In summary, the conversation discusses the concept of equivalent force systems and how to determine if two systems are equivalent. The main criteria for equivalence is that the resultant force and moments about a point are the same for each system. The conversation also mentions that systems (a) and (b) are not equivalent, but does not provide an explanation for why. The conversation ends with the suggestion to compare systems (a) and (c) to determine their equivalence.
  • #1
jegues
1,097
3

Homework Statement


See figure


Homework Equations


[tex] \sum F_{x} = 0[/tex]

[tex] \sum F_{y} = 0[/tex]


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,

[tex] M_{a} = 63N.m[/tex]
[tex] M_{b} = 35N.m[/tex]

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

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  • #2
No figure attached.
 
  • #3
PhanthomJay said:
No figure attached.

Sorry about that, it should be in the OP now.
 
  • #4
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'?
 
  • #5
That's all I needed!

Thank you!
 

1. What is an equivalent force system in statics?

An equivalent force system in statics is a set of forces that has the same overall effect on a body as the original set of forces. This means that the equivalent force system will produce the same result in terms of translation and rotation of the body.

2. Why are equivalent force systems important in statics?

Equivalent force systems are important because they allow us to simplify complex systems of forces into a single, equivalent force. This makes it easier to analyze and calculate the overall effect of the forces on a body.

3. How is an equivalent force system determined?

An equivalent force system can be determined by using the principle of transmissibility, which states that a force can be moved along its line of action without changing its effect on a body. This allows us to move and rotate forces to create a new, equivalent system.

4. Are equivalent force systems only applicable to static situations?

No, equivalent force systems can also be used in dynamic situations. However, in dynamic situations, the forces may also have an effect on the acceleration of the body, in addition to its translation and rotation.

5. Can two different systems of forces have the same equivalent force?

Yes, it is possible for two different systems of forces to have the same equivalent force, as long as they produce the same overall effect on a body. This is because the equivalent force only takes into account the overall effect of the forces, not the individual forces themselves.

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