Work, Energy, and Power

In physics, work is the transfer of energy by a force acting through a distance. The precise definition is W = F·d·cos(θ): the product of the force, the distance, and the cosine of the angle between them. Power then measures how quickly that work is done, P = W ÷ t, in watts.

Why the Cosine Matters

Forces have direction, and only the component along the path of motion contributes to work. A force applied straight down on a cart rolling horizontally does zero work on it, no matter how hard you push — the cart's motion never aligns with your push. The cosine factor encodes this geometry.

Practical Numbers

Lifting a 10 kg box 1 meter requires about 98 J of work. A 60 W light bulb converts 60 J of electrical energy per second. Climbing stairs for a minute at moderate pace does roughly 5,000 J of work — about the same energy the bulb uses in 83 seconds. Watts and joules are everywhere once you know how to count them.