Problem-Solving: Mechanics

Choosing Your Law

Expert problem-solvers do not start with formulas. They start by choosing a law: does this need Newton, energy, or momentum?

General strategy: Draw a diagram with all forces and axes, list knowns, choose the principle, solve algebraically, then check units.

Dimensional analysis requires every equation to be consistent:

$$[F] = \text{kg}\cdot\text{m/s}^2, \quad [E] = \text{kg}\cdot\text{m}^2/\text{s}^2$$

Pitfalls & Multi-Stage

Mechanics problems often chain different laws across different stages. Watch out for these traps:

• Vector sums: Remember $\vec{F}_{\text{net}}$ is a vector sum, not a scalar sum.
• Non-conservative work: Do not use energy conservation when non-conservative forces do work.
• Sign conventions: Confusing $g = 9.8$ with $g = -9.8$ depends entirely on your axis choice.

Collisions: Applying energy conservation across a sticking collision fails. Perfectly inelastic impacts destroy kinetic energy; only momentum bridges that moment. Split the problem at the collision and switch tools.

Stuck? Count equations and unknowns. Fewer equations than unknowns means you need another physical principle.