What a learner can do afterwards
- Computes the work done by a varying force as an integral along a stated path
- Derives the work-energy theorem from Newton's second law
- Explains why only the component of force along the motion contributes
1 · Read
Last stop drag pushed against every metre you moved and drained energy of motion. In physics, work means energy handed over by a force during a displacement. When the force varies, you chop the path into tiny steps, multiply force by each tiny step, and add them all. That sum is the integral of force along the path. For a steady push along the motion the sum collapses to force times distance.
Only the part of the force pointing along the motion counts. A push with the motion does positive work, a push against it does negative work, and a sideways push at right angles does zero work. The angle between force and step decides everything.
Stretch a spring and the pull grows with the stretch, so force times distance no longer works. Integrating the growing force over the stretch gives the stored work. That is exactly how you find the work of pulling a spring from its natural length.
Add up the work of every force and you get the net work, which equals the change in kinetic energy. Speeding pushes add energy of motion, and resisting pushes remove it. That link is the work energy theorem, derived straight from Newton, not quoted.
Work is the integral of force along the path, and net work equals the change in kinetic energy.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.