# 8.2 Power

 Page 1 / 2

## Power

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

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,

$P=\frac{\Delta W}{\Delta t}.$

This can be written as:

$\begin{array}{ccc}\hfill P& =& \frac{\Delta W}{\Delta t}\hfill \\ & =& \frac{\Delta \left(F·d\right)}{\Delta t}\hfill \\ & =& F\frac{\Delta d}{\Delta t}\hfill \\ & =& F·v\hfill \end{array}$

The unit of power is watt (symbol W).

## Investigation : watt

Show that the W is equivalent to $\mathrm{J}·{\mathrm{s}}^{-1}$ .

## 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. $\begin{array}{ccc}\hfill P& =& F·v\hfill \\ & =& \left(10\phantom{\rule{0.166667em}{0ex}}\mathrm{N}\right)\left(1\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\right)\hfill \\ & =& 10\phantom{\rule{0.166667em}{0ex}}\mathrm{W}\hfill \end{array}$
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.

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  $\mathrm{km}·{\mathrm{hr}}^{-1}$ to 60 $\mathrm{km}·{\mathrm{hr}}^{-1}$ 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  $\mathrm{km}·{\mathrm{hr}}^{-1}$ to 60 $\mathrm{km}·{\mathrm{hr}}^{-1}$ in 4 s.

what does the word emitted mean?
to be ejected or released
Khathutshelo
Ok thanks
Mwinga
what are the hooke laws
what do really asked in exam
Which equation do u wanna balance
Rifumo
i tried to write it but my phone just can't write it Cr2 O72-(aq) + H2S (aq) Cr3 (aq) + S(s)
Brian
show is the equation
Pride
us
Pride
hello. what is the difference between a primary, secondary and tertiary alcohol
primary the C=bonded to 1 Carbon atom.... secondary=bonded to 2 carbon atoms tertiary=bonded to 3 carbon atoms
Christina
Christina
thanks Christina
Baningi
My pleasure
Christina
Thank you Christina. This is very helpful 😀👍👍💯
Thokozani
💯💯
Thokozani
Anytime Thokozani
Christina
How to calculate pH?
Thabo
thank you guys i didn't know about the primary, secondary and tertiary alcohols
Brian
thank you Christina
Brian
Hey guys which topic does AC nd DC generator falls
Phumelele
electrodynamics
Christina
thank you
Phumelele
can somebody help me with functional isomers
function isomer has the same molecular formula but different functional group
Thokozani
what's momentum
the product of an objects mass times velocity. it is mainly prevalent in collisions.
tyrique
momentum
Sesethu
in order to produce an interference pattern, the waves used must be what?
Methane contains C and H. This compound is
ketones's functional group
Why does the carboxyl group have acidc properties?
carboxylic acids
tyrique
Besides improving appearance what is another reason why medal is electro plated
Reunity
thanks
Elizabeth
what is different between Dependent variable and independent variables
Elizabeth
difference between A.c and D.c
Gerrard
AC has slip rings DC has split rings commutator
Mohludi
to avoid rust and to improve strength and conductivity
Shubham
the variable whose value doesn't depend on other is known as independent variable ex time
Shubham
are UV rays dangerous?
no
Lianda
what's this?
Lianda
if there is extensive exposure, it can lead to skin cancer
tyrique
yes depend upon their intensity
Shubham
i hv a problem with this chapter because i also have problem with Newton's laws of motion
I have a problem with calculation in Newton's law of motion
Vuyokazi
me also VuyokAzi
Amahle
what's the question
Christina
Which area in particular?
Kevo
just get the hang if free body diagrams,know the directions.
Muregu
I know how to draw free diagram I have a problem with calculation in second law
Vuyokazi
what is the wave model of atom ?
guys what is momentum
Luvelo
@Luvelo... Momentum is the product of an object's mass and its velocity.
Christina
the model based on wave nature of electron
Shubham
Can you state the Doppler effect in words
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
Cassiey
the change in frequency of the sound detected by a listener because sound source and listener have different velocity
Elizabeth