Work
In physics, a force does work when it moves something along the direction of the force:
W = F × d × cos θ
- F: force, in newtons
- d: distance moved, in meters
- θ: angle between the force and the motion
Work is measured in joules (J): 1 J is a force of 1 N acting over 1 m. In US customary units, 1 foot-pound (ft·lbf) equals 1.356 J.
- At θ = 0°, all the force helps: W = F × d.
- At θ = 90°, the force does no work, like the force holding a bag while you walk.
- At θ = 180°, the work is negative, as with friction or brakes, which remove energy.
Power
Power is the rate of doing work:
P = W ÷ t
measured in watts (W): 1 W is 1 J per second. One mechanical horsepower is about 745.7 W.
Worked example
You push a cart with a force of 50 lbf (222 N) over 30 ft (9.14 m), in the direction of motion, in 20 seconds.
- Work: 222 × 9.14 × cos 0° = 2,034 J, or 1,500 ft·lbf.
- Power: 2,034 ÷ 20 = 101.7 W.
- In horsepower: 101.7 ÷ 745.7 = 0.136 hp.
If you pushed at a 30° angle with the same force, only cos 30° = 87% of it would count, and the work would be 1,761 J.
Everyday power levels
| Activity or device | Power |
|---|---|
| Person at rest (metabolism) | about 100 W |
| Brisk cycling, recreational | 100 to 200 W |
| Trained cyclist, one hour | 250 to 400 W |
| Microwave oven | about 1,000 W |
| Small car engine | about 75,000 W (100 hp) |
Work and energy
The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Lifting a mass m by a height h does work m × g × h, stored as potential energy. Climbing a 10 ft flight of stairs, a 160 lb person does about 2,170 J of work; doing it in 5 seconds means about 430 W, more than half a horsepower.
Units
| Quantity | SI unit | US customary |
|---|---|---|
| Work, energy | joule (J) | foot-pound (ft·lbf), BTU |
| Power | watt (W) | horsepower (hp), ft·lbf/s |