Resolving forces into components

Resolving forces into components

Force components are useful because Newton's second law can be applied separately along perpendicular axes. On an incline or for a pull at an angle, choose axes that make the problem simpler, often parallel and perpendicular to a surface. Resolve only the forces at an angle to those axes; then add components along each axis with signs. A zero net force perpendicular to a surface does not mean every force is zero; it means the perpendicular components balance. The component method turns a crowded sketch into two one-dimensional equations with clear physical meaning.

Work it through

A 10 N force at 37° above horizontal has components 8 N right and 6 N up. If another horizontal force is 5 N left, the horizontal net force is +3 N. The vertical component may be balanced by another force, depending on the system. Do not combine magnitudes before deciding whether they act on the same axis.

Mastery target

Choose axes, resolve angled forces, add signed components and use the resulting net component in a Newton's-law equation.