← Unit 3: Work, Energy, and Power
Work as an Integral
When force varies with position, work is computed as the integral of force with respect to displacement, not simply force times distance.
Overview
W = ∫F(x)dx, generalizing the simple W=Fd formula to variable forces like springs (F=-kx). For a spring stretched from 0 to x, W = ∫₀ˣ kx dx = ½kx², matching the familiar spring potential energy formula.
Practice Quiz
Question 1 of 1Score so far: 0/0
Why is W=∫F(x)dx needed instead of simply W=Fd for a spring's force F=-kx?