A wrong free body diagram makes every subsequent line wrong
Almost every mechanics problem that goes wrong went wrong at the diagram. The algebra afterwards is usually fine. Getting the forces, the reactions and the sign convention right is where the difficulty concentrates and where the partial credit is.
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Isolate the body, then draw every force acting on it
The discipline is choosing what to isolate and then being exhaustive about what acts on it. Missing a reaction at a support, or including an internal force that cancels within the body, produces equations that cannot be solved or that solve to the wrong answer. Both are setup errors and both are diagnosable from the diagram alone.
Sign conventions are the second recurring problem. Choosing one and applying it consistently matters more than which one you choose. Students who switch convention partway through get an answer with the wrong sign and no way to find where it happened.
In dynamics, the extra step is deciding which approach fits: Newton's second law, work and energy, or impulse and momentum. Problems asking about velocity over a distance suit energy methods; problems asking about velocity over a time suit impulse. Recognizing that saves a great deal of algebra.
- Free body diagrams drawn before any equation is written
- One sign convention, applied throughout
- The right method chosen for what the question asks
- Working shown so partial credit is available
What we work on
Your own coursework, on teaching examples
- Free body diagrams and equilibrium problems
- Trusses, frames and internal force analysis
- Stress, strain and deflection
- Dynamics: choosing between force, energy and momentum methods
- Lab reports and design project write-ups
We explain the method. You solve your own problems
- We do not solve problem sets you will submit.
- We do not produce calculations, drawings or designs for you.
- We do not sit or assist during any exam or timed assessment.
- We do not supply solution manuals or completed work.
- We teach the method on teaching examples, then you apply it.
Mechanics underpins structural and mechanical design, where errors have physical consequences. This is one of the subjects where working through it yourself matters beyond the grade. Read the full policy.
Frequently Asked Questions
Usually a missed reaction at a support, or including forces internal to the body you isolated. Work through the supports systematically: what can each one resist, and therefore what reaction does it provide. Being exhaustive about supports fixes most of it.
Look at what the question asks. Velocity as a function of position suits work and energy. Velocity as a function of time suits impulse and momentum. Acceleration at an instant suits Newton's second law directly. Choosing well can turn a page of algebra into three lines.
Which one you pick does not; consistency does. Choose, state it on the diagram, and apply it everywhere. Answers with the right magnitude and wrong sign are almost always a convention that changed partway through.
For working. Mechanics rubrics award partial credit heavily, and an unsupported answer cannot earn them. It also makes your own errors findable, which is what matters under exam conditions.
With the documentation, the justification and the analysis write-up, yes. We do not produce designs, drawings or calculations you submit. The rationale is usually where the points are anyway, and it is where students spend least time.
Send the problem and your diagram
Even a wrong one. The diagram is usually where we can see exactly what went wrong and why.
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