# Resultant Vectors and Equilibriant Vectors

1. Jan 19, 2013

### ME_student

Question: How do the Equilibrant and Resultant vectors relate to each other?

My answer: They relate to each other because they are both vectors. Equlibrant is when forces are equal, but opposite each other, thus brings an object to an equilibriam state. A resultant vector is two or more vectors acting on an object in opposite directions which will cancel the forces making it zero.

So do they both mean the same thing?

2. Jan 19, 2013

### haruspex

No, that's equilibrium. The equilibrant is a force - what force?

3. Jan 19, 2013

### ME_student

Well, that is what it says in my prelab assignment. It says, "A force equal to but opposite in direction to the resultant is called the equilibrant, E, and is that force which, together with the resultant force, will produce equilibrium, i.e. E+R=0.

4. Jan 19, 2013

### haruspex

Yes, but you wrote "Equilibrant is when forces are equal", which describes a circumstance, namely, equilibrium.
The equilibrant should properly be defined as 'that force which if added to the system would produce equilibrium'. From Newton's laws it follows that it is equal and opposite to the resultant.

5. Jan 19, 2013

### agm1984

the resultant force is kind of like the total of all vectors, and the equilibrant is 180 degrees around and is the force that would balance the resultant

a perfect example is a force table. 0 degrees at north, 90 east, 180 south, 270 west.

force 1 = 50 newtons @ 35deg
force 2 = 200 newtons @ 120 deg
force 3 = 19 newtons @ 200 deg

if you calculate the resultant of each individual force and add those resultants together using vector addition (tip to tail) the equilibrant will be the vector that connects them into a closed polygon.

or in actuality you would calculate the sum X and Y forces and the resultant of that is the "resultant force" and the equilibrant is the "resultant force plus 180 degrees"

ie: if your table pivots in the middle and has some weight hanging off one side it will be lopsided, and the equilibrant will be the force that makes it level again, and just to clarify the resultant is the direction and magnitude of the lopsidedness.

6. Feb 2, 2013

Okay thanks.