Physics Force Application

Linear Algebra (Matrices) · Axiom Academy

A force has a size and a direction — so it's a vector. Add them, balance them, and let one do work, all with the same vector arithmetic from this unit. Every push and pull around you is a vector . Combine two of them and you get the net force ; make them cancel and the object holds still ; pull something along and the part of the force in the direction of motion does the work — three moves, one toolkit. The net force is the sum of the forces Two people shove a heavy crate. Each push is a vector; the crate feels their vector sum — add them componentwise (or tip-to-tail). Swing the second push around and watch the resultant change. Equilibrium means the forces sum to zero A sign hangs from two ropes, each pulling with . It only stays put when everything cancels: . Drag the rope angle until the leftover net force vanishes. Work is the dot product of force and displacement Now move something. Pull a sled with a rope held at angle . Only the part of the force along the motion counts, and that's exactly the dot product: . Tilt the rope and watch the work. One idea — a force is a vector — and three moves: add them for the net force ( ), set the sum to zero for equilibrium ( ), and dot force with displacement for work ( ). The same vector arithmetic runs cable-stayed bridges, robot grippers, and rocket thrust.

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.