Plain-English Meaning
If you push a box sideways 5 m with 10 N of force — in the same direction — you do 50 J of work. But if the force is perpendicular to movement (like a normal force), it does zero work. The cos θ factor accounts for the angle between force and motion.
Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.
Deeper Explanation
W = ∫F·ds (line integral); for constant force at angle θ: W = Fd cos θ. The work–energy theorem states W_net = ΔKE. Conservative forces (gravity, springs) store work as potential energy; non-conservative forces (friction) dissipate it as heat.
Worked Example
Problem: A 500 N force acts at 30° to displacement. The box moves 8 m. How much work is done?
- W = Fd cos θ
- W = 500 × 8 × cos 30°
- cos 30° ≈ 0.866
- W = 500 × 8 × 0.866 = 3464 J
Result: W ≈ 3464 J
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At A Glance
Category: Mechanics
Levels covered: High School, College, Masters, PhD
Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.