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Statics Problem-Solving Methods & Applications

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  • 0:02 Static Equilibrium
  • 1:24 Static Problem Solving Methods
  • 4:35 Applications
  • 5:38 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Find out exactly what requirements need to be satisfied for a physics problem to be classified as a statics problem. Then learn the steps you take to solve these statics problems.

Static Equilibrium

What sort of images come to your mind when I tell you a force is acting on an object? It might be something flying through the air, sliding down a slope, or being pushed along the ground. What about an object that's sitting still, though? Imagine something like a chair stationary on the ground, or a picture frame hanging on the wall. Even though those two objects aren't moving, they still have forces acting on them.

When an object is stationary and both the sum of all the forces and the sum of all the torques acting on it are equal to zero, it is said to be in static equilibrium. The torques and forces must both equal zero because they are trying to accelerate the object. Forces try to create a linear acceleration, and torques try to rotate the object with an angular acceleration.

When we have a physics problem that asks us to find the forces or torques acting on an object in static equilibrium, we call it a statics problem. There is another type of equilibrium called dynamic equilibrium, but we aren't working with that here. Just so that you know the difference -- an object is in dynamic equilibrium when the sum of the forces and the sum of the torques are equal to zero and the object is moving at a constant velocity.

Static Problem-Solving Methods

Once you're tasked with solving a statics problem, how do you actually go about doing it? There are several steps you can follow to make the problem as easy as possible for you.

Step one: Read the problem. This might seem like a trivial step, but many mistakes are made by skimming through the problem and assuming you know what to do. Always carefully read through the problem to make sure you know what it is asking of you.

Step two: Make a drawing. Specifically, what you want to draw is something called a free body diagram, which is a simple visual representation of the object in question from the statics problem. You'll also draw arrows showing the directions of all the forces and torques acting on it. Free body diagrams can be used for more than just static equilibrium problems, but they are very useful here for helping you visualize the problem.

Step three: Name the forces and torques. At some point, all these forces and torques acting on the object we drew will come up in our equations to solve the problem. They need names so you can keep track of which variables you're working with in your equations. It's normal to put the names of the forces and torques next to the arrows representing them on the free body diagram.

Step four: Make a plan. Look at your drawing, reread the problem, and ask yourself what information do I have, and what do I need. Get an overall idea of what you need to do. Are you looking for forces, torques, how many of them, in what directions, and so forth? If you just start writing down formulas without getting a plan, you will probably end up making the problem more complicated than it needs to be.

Step five: Write your formulas down. Now it's time to actually write those formulas on the paper. Remember, in static equilibrium, we know that the sum of the forces and the sum of the torques both equal zero. For a problem in two dimensions, we can break up the sum of the forces into x (horizontal) and y (vertical) components.

torque sum equation

horizontal force sum equation

vertical force sum equation

When you have your formulas written down, look at the number of unknown variables you have. If you need to solve for every unknown variable, the number of formulas you have should at least equal the number of unknown variables.

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