1. Read the problem and form a strategy
The first thing I do is read the problem and look for what information they gave us and what they are asking for.
In static equilibrium problems, they usually give a diagram of the system with dimensions and the mass of an object, then ask you to solve for a force, like tension.
This isn’t always the case as seen in this example problem, where they give you the tension in the rope, then ask you to solve for the mass of the object.
2. Draw a free-body diagram (FBD)
Now that we know what they are asking for, we need to draw a free-body diagram.
If there is only one mass, you will only need one FBD, as seen in this example problem.
If there is more than one mass, you will need to draw an FBD for each mass, as in this example problem.
Start by representing the mass as either a point or a line.
If your mass is a beam, mark down how your beam is connected to the wall or floor.
This could be a pin joint, a roller joint, or a fixed connection like a weld.
Now that you have your mass represented on your FBD, write down and label all of your forces acting on the object.
3. Write out your equilibrium equations
Now that you have an FBD you need to decide which equilibrium equation you want to use first.
I suggest that before you start writing out your equations, think about how many unknowns you will have in each equation.
For beams, it is usually easier to start with a rotational equilibrium equation.
For point masses, you only have the option to use translational equilibrium equations, since all the forces act through the same point.
4. Solve for your unknowns
Now that you have your equilibrium equations, you can solve for the unknowns.
The best-case scenario is when you have an equation with a single unknown.
In that case, you can rearrange that equation for the unknown and plug in your numbers.
If you have two equations with two unknowns, you will need to use another method, like substitution, to solve for your unknowns.
Check out these YouTube videos to see solved examples
When I was in engineering school, I always started studying by watching YouTube videos (shoutout The Organic Chemistry Tutor).
Seeing other people solve problems helped me understand the thought process behind the steps to the solution.
Once I got the basics, I would start solving practice problems myself.
I am working on a Physics video series on YouTube where I go through theory and practice problems.
Check out these videos below!
Translational Equilibrium Videos
Rotational Equilibirium Videos
Want extra practice problems with solutions? Check out my eBooks
Once you have watched a couple of YouTube videos, it’s time to practice for yourself!
Check out these physics eBooks with practice problems and full solutions.
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