Lesson 1 · 12 min
Work and power
Force through a distance. The rating plate on every motor is this idea, in watts.
Work is a scalar
A force does work when its point of application moves. W = F · Δr = F Δr cosα for a constant force. Only the component along the displacement counts. A centripetal force on uniform circular motion does zero work — it is always perpendicular to dr. A normal force on a stationary contact does zero work. Gravity does work whenever height changes.
One watt is one joule per second. A horsepower is 746 W — a historical unit, still on nameplates.
Worked example
Hoist
- Given: Load 400 kg
- Given: Raise 8.0 m at constant speed in 12 s
Find: Average power the motor must deliver (ideal)
- Work against gravity: W = mgh = 400 × 9.81 × 8.0 = 3.14 × 10⁴ J
- Constant speed means net force on the load is zero; the cable still does this work.
- P = W/t = 3.14e4 / 12
2.6 kW (plus losses — a 4 kW motor is a sane first pick)
Check
You carry a 10 kg crate across a room at constant height and constant speed. Work done by you on the crate?