Will a Particle Remain in Equilibrium if Three Reversed Forces are Removed?

[Final_HB]

Homework Statement

A particle is under the influence of 5 forces. Three of these forces are reversed, and the particle remains in equilibrium. Prove that the particle will remain in equilibrium even if these three forces were removed altogether.

The Attempt at a Solution

My thinking for this is:
With three of the forces gone, the 2 forces (F₁ and F₂ ) left must balance the system if its to remain at equilibrium.
If change of forces occurs, the system will react by moving to a new state of equilibrium.
No reaction means that the 3 forces in the question cancel out each other, and no shift occurs.
If the three forces balance to 0, there is no need to have them as acting on the particle.

Right?

If I am right, Is there any maths way to say this, or a better way to explain what I am trying to say. Thank you in advance.

 

[ehild]

Homework Statement

A particle is under the influence of 5 forces. Three of these forces are reversed, and the particle remains in equilibrium. Prove that the particle will remain in equilibrium even if these three forces were removed altogether.

The Attempt at a Solution

My thinking for this is:
With three of the forces gone, the 2 forces (F₁ and F₂ ) left must balance the system if its to remain at equilibrium.
If change of forces occurs, the system will react by moving to a new state of equilibrium.
No reaction means that the 3 forces in the question cancel out each other, and no shift occurs.
If the three forces balance to 0, there is no need to have them as acting on the particle.

Right?

If I am right, Is there any maths way to say this, or a better way to explain what I am trying to say. Thank you in advance.

You are right, but it can be formulated mathematically. Write up the sum of forces for both cases, and manipulate the equations.

ehild

 

[Final_HB]

Well...

F₁+F₂+F₃+F₄+F₅=0

And for the second:
F₁+F₂-F₃-F₄-F₅=0

taking one away from the other gives us:
2F₁+2F₂=0
So,
F₁+F₂=0

 

[ehild]

Well...

F₁+F₂+F₃+F₄+F₅=0

And for the second:
F₁+F₂-F₃-F₄-F₅=0

taking one away from the other gives us:
2F₁+2F₂=0
So,
F₁+F₂=0

If you mean subtract " by taking one away from the other" the result is 2(F₃+F₄+F₅)=0, so the resultant of these three forces is zero, they can be omitted. And then F1+F2=0, too.

ehild