Lessons · Engineering · work and power
Work is force through a distance; power is how fast
Work is force times the distance moved along the force, W = F × d, in joules. Power is work over time, P = W / t, in watts. One horsepower is 746 W.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A hoist has to lift a 400 kg motor 6 m and the motor on the hoist is rated in kilowatts. Whether it can do it, and how long it takes, is work divided by power, and it decides whether the lift happens before lunch.
How to think about it
Force first, usually a weight, m × g. Times the height it is lifted, for the work. Divide by the time for the power, or by the power for the time. Horsepower is 746 W if the nameplate is in horsepower.
Worked example
W = F × d, force along the motion; P = W / tWork and power.
Lift a 50 kg pump 3 m: F = 50 × 9.81 = 490.5 N; W = 490.5 × 3 = 1471.5 JThe weight is the force; the height is the distance.
Done in 10 s: P = 1471.5 / 10 = 147 WWork over time.
1 hp = 746 W, so that is 0.2 hp. A person can sustain about 0.1 hp all dayThe scale of the number, against something you know.
Your turn
A 30 kg load raised 2 m. Write the work.
W = 30 × 9.81 × = 588.6 J
Solve one, graded on the server
The trap
Counting distance the force did not act along. Carrying a box 100 m along a level floor does no work on the box in this sense; the work was lifting it, and the lift was one metre.