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Now that we understand the relationship between work and energy, we are ready to look at a quantity that defines how long it takes for a certain amount of work to be done. For example, a mother pushing a trolley full of groceries can take 30 s or 60 s to push the trolley down an aisle. She does the same amount of work, but takes a different length of time. We use the idea of power to describe the rate at which work is done.


Power is defined as the rate at which work is done or the rate at which energy is expended. The mathematical definition for power is:

P = F · v

[link] is easily derived from the definition of work. We know that:

W = F · d .

However, power is defined as the rate at which work is done. Therefore,

P = Δ W Δ t .

This can be written as:

P = Δ W Δ t = Δ ( F · d ) Δ t = F Δ d Δ t = F · v

The unit of power is watt (symbol W).

Investigation : watt

Show that the W is equivalent to J · s - 1 .

Interesting fact

The unit watt is named after Scottish inventor and engineer James Watt (19 January 1736 - 19 August 1819) whose improvements to the steam engine were fundamental to the Industrial Revolution. A key feature of it was that it brought the engine out of the remote coal fields into factories.

Research project : james watt

Write a short report 5 pages on the life of James Watt describing his many other inventions.

Interesting fact

Historically, the horsepower (symbol hp) was the unit used to describe the power delivered by a machine. One horsepower is equivalent to approximately 750 W. The horsepower is sometimes used in the motor industry to describe the power output of an engine. Incidentally, the horsepower was derived by James Watt to give an indication of the power of his steam engine in terms of the power of a horse, which was what most people used to for example, turn a mill wheel.

Calculate the power required for a force of 10 N applied to move a 10 kg box at a speed of 1 ms over a frictionless surface.

  1. We are given:

    • we are given the force, F =10 N
    • we are given the speed, v =1 m · s - 1

    We are required to calculate the power required.

  2. From the force diagram, we see that the weight of the box is acting at right angles to the direction of motion. The weight does not contribute to the work done and does not contribute to the power calculation.

    We can therefore calculate power from:

    P = F · v
  3. P = F · v = ( 10 N ) ( 1 m · s - 1 ) = 10 W
  4. 10 W of power are required for a force of 10 N to move a 10 kg box at a speed of 1 ms over a frictionless surface.

Got questions? Get instant answers now!

Machines are designed and built to do work on objects. All machines usually have a power rating. The power rating indicates the rate at which that machine can do work upon other objects.

A car engine is an example of a machine which is given a power rating. The power rating relates to how rapidly the car can accelerate. Suppose that a 50 kW engine could accelerate the car from 0  km · hr - 1 to 60 km · hr - 1 in 16 s. Then a car with four times the power rating (i.e. 200 kW) could do the same amount of work in a quarter of the time. That is, a 200 kW engine could accelerate the same car from 0  km · hr - 1 to 60 km · hr - 1 in 4 s.

Questions & Answers

what does the word emitted mean?
Mwinga Reply
to be ejected or released
Ok thanks
what are the hooke laws
Tyriek Reply
what do really asked in exam
Leiyo Reply
hi please help me how to balance redox reactions?
Brian Reply
Which equation do u wanna balance
i tried to write it but my phone just can't write it Cr2 O72-(aq) + H2S (aq) Cr3 (aq) + S(s)
show is the equation
hello. what is the difference between a primary, secondary and tertiary alcohol
Thokozani Reply
primary the C=bonded to 1 Carbon atom.... secondary=bonded to 2 carbon atoms tertiary=bonded to 3 carbon atoms
I hope you're answered
thanks Christina
My pleasure
Thank you Christina. This is very helpful 😀👍👍💯
Anytime Thokozani
How to calculate pH?
thank you guys i didn't know about the primary, secondary and tertiary alcohols
thank you Christina
Hey guys which topic does AC nd DC generator falls
thank you
can somebody help me with functional isomers
Baningi Reply
function isomer has the same molecular formula but different functional group
what's momentum
Luvelo Reply
the product of an objects mass times velocity. it is mainly prevalent in collisions.
in order to produce an interference pattern, the waves used must be what?
Methane contains C and H. This compound is
Juan Reply
ketones's functional group
Moloi Reply
Why does the carboxyl group have acidc properties?
Evi Reply
carboxylic acids
Besides improving appearance what is another reason why medal is electro plated
Elizabeth Reply
it is made of metal
what is different between Dependent variable and independent variables
difference between A.c and D.c
AC has slip rings DC has split rings commutator
to avoid rust and to improve strength and conductivity
the variable whose value doesn't depend on other is known as independent variable ex time
are UV rays dangerous?
Khathutshelo Reply
what's this?
if there is extensive exposure, it can lead to skin cancer
yes depend upon their intensity
i hv a problem with this chapter because i also have problem with Newton's laws of motion
Kearabetswe Reply
I have a problem with calculation in Newton's law of motion
me also VuyokAzi
what's the question
Which area in particular?
just get the hang if free body diagrams,know the directions.
I know how to draw free diagram I have a problem with calculation in second law
what is the wave model of atom ?
Trazy Reply
guys what is momentum
@Luvelo... Momentum is the product of an object's mass and its velocity.
the model based on wave nature of electron
Can you state the Doppler effect in words
Nombuyiselo Reply
State Coulomb's law in words
the magnitude of the electrostatic force exerted point on each other is directly proportional to the product on magnitude of charges and inversely proportional to the square distance between them
the change in frequency of the sound detected by a listener because sound source and listener have different velocity

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Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
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