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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 = 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

how is ester formed
Aubrey Reply
how is n ester formed
Aubrey
Alcohol reacts with a carboxylic acid
Texas
an athlete with a mass of 70kg runs at a velocity of 45km . determine the athlete's momentum
Lesedi Reply
Is that a velocity or something else
msawenkosi
45km/h i guess
Texas
Change to m/s
Texas
45km/h = 12.5 m/s p=mv =70×12.5 =875 kg.m/s
Thato
what are the measures of the rates of reaction
Lesego Reply
Volume Concentration Temperature Pressure Surface Area
Thato
the principle of superposition of waves
Sfundo Reply
what is work
Kool Reply
is this a group chat
Nobuhle Reply
Hey can y'all define newton's 2nd law
mthebzification
If a resultant force act on an object...the object will accelerate in the direction of a resultant force,the acceleration of the object is directly proportional to the net force and inversely proportional to the mass of the object
mosa
how do you calculate tension force
Bulumko
use the formula Fnet=ma if there is tension connecting two objects
Sboniso
to calculate Tension, usually calculate acceleration first Draw separate free body diagrams for each body. Apply Fnet = ma to calculate Tension
Kevin
Hi people
Paul
how does temperature affect the equilibrium position
Blessing Reply
an increased temperature increases the average kinetic energy thus in turn increases the number of effective collisions........
Lwando
so...which reaction is favored between endothermic and exothermic .when temperature is increased..?
Blessing
exothermic reaction because energy is realised to the surroundings as heat and light energy ....graphical so much energy is realised as reactants to form product and because temperature is high rate of reaction is fast which means there is a successful collision
Code
INTEMENDO - INCREASE IN TEMPERATURE FAVOURS ENDOTHERMIC DETEMEXO - DECREASE IN TEMPERATURE FAVOURS EXOTHERMIC
Thato
an object will continue in a state of rest unless it is acted upon an unbalanced force
Junior Reply
Newton's Law 1
Code
First Newton's Law
Azola
Newton's first law
Surprise
newton first law
Thinavhuyo
Newton's first law
Blessing
when pressure is increased what happen to volume
Siphelo Reply
decreases
Code
care to explain?
Mpati
if pressure is applied to a pistol , the volume will decrease and particles will collide more frequently with the wall of a container .Each time they collide with the wall they exert a force on them .More collision means more force and the pressure will increase , that Boyle's Law
Code
Because the volume has decreased , the particle will collide more frequently with the wall of a container and each time they collide with the wall of a container they exert a force on them.More collision means more force so the pressure will increase , that Boyle's Law
Code
what is the difference between momentum and a change in momentum?
Chavonne Reply
How to name a branched molecule from right or left?
Vadin Reply
What's Free Fall
Senzo Reply
Free Fall means there is no acting force on that object.
Dingaletu
only gravitational force
Dingaletu
no external force acting on an object
Sphiwe
by only force of gravite
Sello
but gravitational force
Sphiwe
true
Lucky
a motion in which the only force acting is gravitational force
Blessing
and an object experiencing free fall is referred as a projectile
Blessing
Do polymers form restrictedly only if compound is saturated, only?
milani Reply
what is a free fall?
Beyanca Reply
is when The Only Force acting On an Object is Gravitational Force
Madman
Thats right
Beyanca
then Why ask when you Know the answer?
Madman
She's just helping those who forgot it...bro
Thato
guys I need help on Getting ready for a last minute test
Kenelioe Reply
what help you need
Neil
we'll I'm in grade 12 so we doing this topic about upac thing
Kenelioe
on What?
Madman
the organic molecule section
Kenelioe
IUPAC NAMING WHICH FUNCTIONAL GROUP YOU CANNOT NAME?SO I COULD HELP YOU
Madman
ester
Sboniso
you should also look at structural isomers. Its crucial that they might add that one. also try and write down the structural formula of all the given compounds on the table
milani

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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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