Is work vector or scalar. Force and displacement are both vector. But, due to complicated math (vector dot products), work is scalar. Power and energy are scalar as well. It does make the math easier. Use arithmetic instead of vector addition. Joules and watts don’t have direction.

The rate at which work is done or energy is consumed. Power The rate at which work is done or energy is consumed.

Power is the rate at which work is done. A “rate” is anything divided by time. Power is work divided by time.

Power = Work / time

Units Work is measured in Joules. Time is measure in seconds.

Common Metric Prefixes

No matter what the problem says, you must use “standard” units in the equation. Distance – meters (m) Time – seconds (s) Force – Newtons (N) Mass – kilograms (kg) Velocity – meters per second (m/s) Power – Watts (W) Work – Joules (J)

James Watt

Watts The unit was names for James Watt, the inventor of the steam engine. Watts engine was better than the current method getting work done (horses). To help sell engines, Watt developed a way to “rate” their abilities.

Rearranging the Power Formula The power formula can be rearranged into three common forms. They are mathematically equal, but they look different and contain different variables. They are useful for different problems, depending on what is “given” in the problem.

Relates Power to Work and Time. Relates Power to Force, Distance and Time. Relates Power to Force and Velocity.

How long will it take a motor, rated at 200 W, to do 1800 Joules of work?

How much power is used to lift a 15 N object upward 4 meters in 20 seconds?

At what speed can a 1000 W motor lift a 25-kg mass?

FYI 1 N is about ¼ pound Helpful with one homework problem.