# 8.2 Power

 Page 1 / 8
• Calculate power by calculating changes in energy over time.
• Examine power consumption and calculations of the cost of energy consumed.

## What is power?

Power —the word conjures up many images: a professional football player muscling aside his opponent, a dragster roaring away from the starting line, a volcano blowing its lava into the atmosphere, or a rocket blasting off, as in [link] .

These images of power have in common the rapid performance of work, consistent with the scientific definition of power    ( $P$ ) as the rate at which work is done.

## Power

Power is the rate at which work is done.

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

The SI unit for power is the watt    ( $W$ ), where 1 watt equals 1 joule/second $\left(\text{1 W}=1 J/s\right)\text{.}$

Because work is energy transfer, power is also the rate at which energy is expended. A 60-W light bulb, for example, expends 60 J of energy per second. Great power means a large amount of work or energy developed in a short time. For example, when a powerful car accelerates rapidly, it does a large amount of work and consumes a large amount of fuel in a short time.

## Calculating the power to climb stairs

What is the power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s? (See [link] .)

Strategy and Concept

The work going into mechanical energy is $W\text{= KE + PE}$ . At the bottom of the stairs, we take both $\text{KE}$ and ${\text{PE}}_{g}$ as initially zero; thus, $W={\text{KE}}_{f}+{\text{PE}}_{g}=\frac{1}{2}{{\mathrm{mv}}_{f}}^{2}+\text{mgh}$ , where $h$ is the vertical height of the stairs. Because all terms are given, we can calculate $W$ and then divide it by time to get power.

Solution

Substituting the expression for $W$ into the definition of power given in the previous equation, $P=W/t$ yields

$P=\frac{W}{t}=\frac{\frac{1}{2}{{\text{mv}}_{f}}^{2}+\text{mgh}}{t}\text{.}$

Entering known values yields

$\begin{array}{lll}P& =& \frac{0.5\left(\text{60.0 kg}\right){\left(\text{2.00 m/s}\right)}^{2}+\left(\text{60.0 kg}\right)\left({\text{9.80 m/s}}^{2}\right)\left(\text{3.00 m}\right)}{\text{3.50 s}}\\ & =& \frac{\text{120 J}+\text{1764 J}}{\text{3.50 s}}\\ & =& \text{538 W.}\end{array}$

Discussion

The woman does 1764 J of work to move up the stairs compared with only 120 J to increase her kinetic energy; thus, most of her power output is required for climbing rather than accelerating.

It is impressive that this woman’s useful power output is slightly less than 1 horsepower     $\left(\text{1 hp}=\text{746 W}\right)$ ! People can generate more than a horsepower with their leg muscles for short periods of time by rapidly converting available blood sugar and oxygen into work output. (A horse can put out 1 hp for hours on end.) Once oxygen is depleted, power output decreases and the person begins to breathe rapidly to obtain oxygen to metabolize more food—this is known as the aerobic stage of exercise. If the woman climbed the stairs slowly, then her power output would be much less, although the amount of work done would be the same.

## Making connections: take-home investigation—measure your power rating

Determine your own power rating by measuring the time it takes you to climb a flight of stairs. We will ignore the gain in kinetic energy, as the above example showed that it was a small portion of the energy gain. Don’t expect that your output will be more than about 0.5 hp.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!