Determining p and q in Equilibrium

In summary, three forces F1, F2, and F3 acting on a particle in equilibrium can be represented by the equations (-3 + p + q = 0) for the i component, and (2p + 3q - 7 = 0) for the j component. Solving these equations simultaneously gives the values of p = 2 and q = 1.
  • #1
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Homework Statement


Three forces F1, F2 and F3 act on a particle.
F1 = (-3i + 2pj)N F2 = (pi + 3qj)N F3 = (qi - 7j)N

Given that the particle is in equilbirum, determine the value of p and the value of q.


Homework Equations



(-3i + 2pj) + (pi + 3qj) + (qi - 7j) = 0

The Attempt at a Solution


Well, its in equilbirum, so I figured all the forces added together would equal 0. Now, because there's more then one unknown, one thing to do is to use is Simultanious Equations, but I'm finding it difficult cause I'm unsure of how to make the simultanious equations, which is meant to be basic at my level =/.

Any hints/help is very appreciated =) However, it is a Sunday after all ;)
 
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  • #2
Since force is a vector, each component must be separately equal to zero. So write two equations: one for the i component, one for the j component. Those are the two equations that you'll have to solve simultaneously.
 
  • #3
Still slightly confused, so essentially is this something along the right lines:
pi = 3i -2pj -3qi -qi +7j

And then the same for qi? But then I'd be wrong, cause it'd be the same statement but with -pi instead of -qi.
 
  • #4
No. First add up all the i components, set that equal to zero. That's one equation. Then do the same for the j components. That's the second equation.
 
  • #5
Ahhh! Thank you for all your help!
-3 + p + q = 0 (All the i values)
2p + 3q - 7 = 0 (All the j values)

-3 + p + q = 2p + 3q - 7
4 -2q = p (We now hav a statement for p, to sub in)

3 - p = q
3 - 4 + 2q = q
q = -3 + 4
q = 1

Sub 1 into:
3 - q = p
p = 2.

And those are the correct answers!
Thank you for all your help! =)
 

1. What is basic equilibrium?

Basic equilibrium refers to a state where the forces or factors acting on a system are balanced, resulting in no net change. This can occur in various systems such as chemical reactions, economic markets, and physical objects.

2. How is basic equilibrium achieved?

Basic equilibrium is achieved when the rate of the forward reaction is equal to the rate of the reverse reaction in a chemical system. In other systems, equilibrium can be reached when the supply and demand are equal in an economic market, or when the forces acting on a physical object are balanced.

3. What is the significance of basic equilibrium in chemistry?

In chemistry, basic equilibrium is crucial for understanding the behavior of chemical reactions. It helps determine the direction of a reaction, the amounts of reactants and products present at equilibrium, and the conditions necessary for a reaction to reach equilibrium.

4. How is basic equilibrium represented mathematically?

In chemistry, basic equilibrium is represented using the equilibrium constant (K), which is calculated by dividing the concentration of products by the concentration of reactants at equilibrium. In other systems, equilibrium may be represented using different mathematical equations.

5. Can basic equilibrium be disturbed?

Yes, basic equilibrium can be disturbed by changing the conditions of the system, such as temperature, pressure, or concentration of reactants or products. This will result in a shift in the equilibrium position, with the reaction proceeding in the direction that relieves the disturbance.

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