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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

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Why is W=∫F(x)dx needed instead of simply W=Fd for a spring's force F=-kx?