The theorem that joins the two halves
Lesson one measured what a force costs. Lesson two measured what motion is worth. The work–energy theorem welds them together: . Read aloud: net work equals the change in kinetic energy. The symbols: is the net work in joules — every force's contribution added up, not just the one you like; (Greek delta) means change in; is the mass in kilograms; and the subscript convention is the one you have used since kinematics — (v-nought) is the speed BEFORE, with no subscript is the speed AFTER, both in m/s.
The sign carries the story, and it is final minus initial, always. Speed up, and : the net work is positive, something paid in. Slow down, and the net work is negative — friction and brakes are the usual withdrawers. Cross a level floor at a constant speed and the net work is exactly zero, no matter how tired you are.
One trap deserves naming before you meet it: is not . Difference the squares; never square the difference. Check it once with 10 and 6 — 64 against 16, and the two answers are not even close.
- = Net work (energy)
- = Mass (mass)
- = Final speed (speed)
- = Initial speed (speed)
- = Kinetic energy (energy)
- = Mass (mass)
- = Speed (speed)