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What Is Static Equilibrium?

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  • Written By: E.A. Sanker
  • Edited By: John Allen
  • Last Modified Date: 22 September 2014
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Static equilibrium is a term used in physics to describe a situation in which the total forces acting on an object at rest add up to zero. In other words, the forces pulling the object in different directions balance out, causing the object to remain motionless. For an object to be in static equilibrium, it must also be in translational equilibrium and in rotational equilibrium, meaning that the external forces and external torques acting on the object must sum up to exactly zero.

In physics, forces of movement are often described in terms of vectors. A vector is an abstract mathematical concept used to represent both the direction and magnitude of a force. If a crate were being pulled a certain distance to the left, for example, the vector would indicate both the direction of the force and the distance the crate was pulled.

Newton’s first law of motion states that an object will remain at a constant velocity if the sum of vector forces on that object is zero. Objects at rest will stay at rest unless acted upon by a force, and objects in motion will, likewise, stay at the same velocity unless acted upon. The vector sum is also called the resultant force, or net force.

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In a case of static equilibrium, forces are acting on an object, but the vector sum of all forces acting on that object is zero. This means that opposing vectors cancel each other out exactly, resulting in zero net force on the object. Although forces are present, the object remains motionless. To continue the example given above, if the crate were being pulled both left and right simultaneously with exactly the same amount of force and exactly opposing torque, all vectors would be opposed exactly to each other and the crate would not move. It would be in static equilibrium.

When the external forces acting on an object cancel each other out, the object is said to be in translational equilibrium, the first condition necessary for static equilibrium. The second condition is rotational equilibrium. In rotational equilibrium, the net torque, or rotational force, acting on the object must be zero. If, for example, the crate is being pulled left and right but is also being twisted around an axis, it would not be in static equilibrium, because torque would cause it to move. An equal and opposite force of torque would be required to set the crate in rotational equilibrium.

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David09
Post 4

@Charred - Yeah, a lot of physical objects function in static equilibrium. Basically, if it’s not flying off your desk or moving one way or another, you can argue that it’s in a state of equilibrium. A simple picture hanging on the wall would be an example.

I vaguely recall static equilibrium from my physics course in college. All I remember is that I needed to use a lot of trigonometry, because when calculating forces acting on an object, there was a horizontal component and a vertical component to each force.

I needed to use sines, cosines and tangents in some situations, but I don’t recall the exact formulas themselves.

Charred
Post 3

@nony - I had to help my daughter with her 12th grade physics this year so I think I can weigh in, although I am by no means an expert.

The static equilibrium definition is neither good nor bad. As a matter of fact, one example of static equilibrium is your chair at rest.

While gravity is pulling the chair down, physicists describe something called normal force acting “up” against the chair which is balancing it out. I remember this example from one of my daughter’s static equilibrium problems.

Now surely you can’t argue that the static equilibrium in this case is bad in any sense of the term. If it weren’t for the normal force, the chair would keep going down; if it weren’t for gravity, well obviously you’d have a flying chair.

A dynamic equilibrium example would be a bicycle in balance riding at a steady speed.

nony
Post 2

@allenJo - Is static equilibrium good or bad? I ask because, as with the job example you gave, the term has somewhat of a negative connotation.

I do agree that people talk about being in a state of equilibrium as being a bad thing. I don’t know myself; I tend to think that it’s neutral, depending on the context.

Maybe static and dynamic equilibrium are what people are thinking about; static is bad, dynamic is good.

allenJo
Post 1

While I didn’t exactly enjoy physics in high school, I can’t deny the fact that it was one of the most relevant science classes I ever took. So much of what you learn about in physics applies to everyday life.

It deals with motion, gravity, momentum, inertia – and here, static equilibrium. Now if you’ve ever played a game of tug-of-war, and you played against a team that was equal and opposite you in strength, you’ve experienced static equilibrium.

If neither of you could move the rope past the center line (effectively a tie) then you were in such an equilibrium state.

I think that static equilibrium examples can be found in other contexts besides tug-of-war however. For example, if you’re at your job, trying hard to get ahead, but there are counteracting forces keeping you down, then you are in equilibrium. You may start wondering if it’s time to move on.

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