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Power and the watt

Flor hauls a box of tiles up a ladder, doing 600 J of work in 10 s.

Comparing her with a second mover needs the second mover. A single number for her own transfer would settle every compare at once. What is that number?

Split her climb into seconds. 600 ÷ 10 = 60. Flor transfers 60 J each second.

Flor's climbquantityvaluework done600 Jtime taken10 senergy each second60 J
600 J over 10 s is 60 J each second.

That number, the joules transferred each second, measures how fast her transfer runs: it is her rate of energy transfer.

The rate of energy transfer is called power.

Power has its own equation: P = W/t, where W is the work done in joules and t is the time taken in seconds.
The equation, on Flor's numberssteplineequationP = W/tsubstituteP = 600 ÷ 10resultP = 60 W
The same move as an equation: P = W/t.

Power is measured in watts. One watt is one joule transferred each second. Flor's power is 60 W.

A 60 W light bulb converts 60 J every second: the same rate as Flor's climb.

Dov's hoist does 1800 J of work in 24 s. Calculate the hoist's power.

Write down the values in the question:

W = 1800 J, t = 24 s; P = ?

Write down the equation:

P = W/t

Substitute in the values, and calculate:

P = 1800 ÷ 24 = 75

The hoist's power is 75 W.

Edda's winch does 240 J of work in 30 s. Enter the winch's power in watts.

A 500 W motor is running. How much energy does it convert each second?

One watt is one joule transferred each second.

The motor's power is 500 W.

So the motor converts 500 J each second.

The motor converts 500 J every second it runs.

A desk fan is rated 45 W. Gael says: 'The fan converts 45 J of energy every second.' Is he correct?

A space heater converts 4400 J of energy in 80 s. Enter its power in watts.

Careful with the symbol W: it does two jobs. In P = W/t, the capital W is the work done, in joules: the same W as in W = Fd.

The watt's symbol W is different: it is written only after a number, like 60 W. A W after a number is the unit; the W in the equation is the work.

The two jobs of the symbol Wwhere it appearswhat it meansin P = W/tthe work done, in joulesafter a number, like 60 Wthe watt, the unit of power
One letter, two jobs: the equation's W is work; the W after a number is the watt.

Your turn

A dishwasher's heating element transfers 4500 J to the water in 90 s. Enter the element's power in watts.

A hoist's test sheet carries two lines: 'motor rating: 60 W' and 'lift record: W = 300 J, t = 5 s'. Which entry is the work done during the lift?

Which statement says what one watt is?