E.T.I. Physics · Tecnológico de Monterrey

Worked solutions

One problem per page, each solved the same way: derive the formula from first principles, test it against the cases you already know, and put numbers in only at the very end. Every page is something you can push on, not something you only read.

drag the sliders — the formulas are live, not pictures

Problems

Pick one

Two cables, one weight, any two angles

Statics

A weight hangs from a point held by two cables at different angles. Find both tensions as a formula in W, θ_l and θ_r — then differentiate it to find where the tension is smallest, and why a swinging load does not behave the way that suggests.

T_r = W cos θ_lsin(θ_l + θ_r) T_l = W cos θ_rsin(θ_l + θ_r)

Open the derivation → 1 live instrument · free-body diagram, equilibrium checks, sensitivity plot

Factoring, on the board

Algebra toolkit

Every basic method — common factor, grouping, difference of squares, perfect squares, both trinomials, cubes — in marker colour, so you can follow where each piece went. Then the part that matters: factoring is how you prise an unknown out of a statics system when it is stuck in two terms at once.

ka + kb = k(a + b)

Open the toolkit → 5 simulations · area model, geometric proof, trinomial inspector, projectile roots, step-by-step isolation

More on the way Each new problem gets its own page and shows up here. Same method every time: a formula you can reuse, not an answer you have to redo.

How these are written

Formula first, numbers last

No numbers until the end. Substituting early hides the structure. A formula survives every set of inputs; an arithmetic answer survives exactly one.
Every step says why, not just what. The grey line under each move names the operation and the condition that makes it legal.
Limit cases are part of the solution. A derived formula is worth nothing until it reproduces the cases you can already check by common sense.
Check against the starting equations, never against the formula you just derived — otherwise you are only testing your algebra against itself.
Then push further. Differentiate it, take a limit, let something move. The formula answers questions the original problem never asked.

Interactive, on purpose

Each page carries live instruments: drag the inputs and the diagram, the numbers and the checks all move together. Not decoration — the point is that you can try to break the formula and watch it refuse.

stuck on the algebra? start with the factoring page

E.T.I. Physics · Anuar Kafuri Zarzosa · Tecnológico de Monterrey