WORK, ENERGY & POWER

Work is a very normal term, usually one we dislike; "clean up your room !", "mow the lawn !" etc.

This word of "work" brings to mind pushing, pulling, walking back and forth. The very unusual thing about the day-to-day usage is that it is almost identical to the Physics usage of the term.

"The WORK done on an object, is the product of the average force on it and the distance travelled in the direction of the force."

Notice; the work is done on an object, like a lump of wood during wood stacking, by something which exerts a force ( you on the wood ). This force must then proceed to move it through a distance in its direction.

You are stacking wood.

In section A, lifting the wood, you are doing work on the log as the force you exert is in the same direction as the distance travelled.

In section B, apart from a slight amount of force to start moving it along the dotted line, you are doing very little work on the log as the lifting force you exert is not in the direction of travel.

In section C, gravity does work on the log.

In VERY simplistic terms
 
 

The unit of work in the modern system is the joule J . ( Very old units include the calorie, BTU and the erg. )
 
 

GRAPHICALLY


 
 

Work has no sense of direction. We do not ascribe arrows to work or energy.

Distance is used rather than displacement in the simple definition because the force acting may take a windy path. You are literally doing work on the pen when you push it writing. The total path taken which is important is the distance rather than the displacement.
 
 

"ENERGY is the ABILITY of an object to do work for whatever reason."

This again sounds like common sense, but stored energy in whatever form has the same units as work and can do, numerically, that amount of work.

Energy comes in various forms;
 


 

Interchangeability of the energies ;

Like momentum, the work-energy idea turns out to be a conservation law. Whenever a process occurs, energy does work and turns into a new form of energy or energies.

When all the forms of energy before and after any process are added we find exactly the same number.
 

PRINCIPLE OF CONSERVATION OF ENERGY; " In any closed system, the total amount of energy remains constant regardless of any process which takes place."

Again, physicists would like to know why, - it is linked to momentum and mass is also a form of energy. ( OK - what is energy ? )

GRAVITATIONAL POTENTIAL ENERGY;

In falling through a height "h" which is in the same direction as the force, the work done by gravity is

work done = force.dist = Mg.h

thus Grav. Pot. Energy Ep = Mgh

This is a stored energy available to be converted into movement energy on release. The Hydro uses this energy in the form of stored water which is released, converts first to kinetic energy then to electrical energy which is distributed around the State.

KINETIC ENERGY; " Energy available because of the object's motion".

Consider a mass, m, which is moving with a speed , v, and does work which brings it to rest.

The unbalanced force, F, which it exerts in doing the work is, by Newton's Third Law also exerted on it , bringing it to a halt.

Funbal = ma

so, Work done = Funbal . dist = mas

( we are assuming all of this takes place in a straight line so that distance and displacement are essentially the same )

Using 2as = v2 - vo2

we get mas = 1/2 .mv2 = Work done

Ek = Kinetic energy = 1/2 mv2

All forms of energy can have such formulae worked out for them !
 
 

Eg 1; A swing oscillates through a height of 3m. How fast is the little girl going at the bottom of the swing ?

Soln; This movement is not in a straight line so we must rely on conservation of energy to see how fast the girl is going. We must assume that no energy is turned into heat or other less easily calculated forms.

In swinging, the energy changes from Grav. Pot . Energy to Kinetic Energy. So

Ep lost = Ek gained ( cons of energy )

mgh lost = 1/2 .mv2 gained

thus, gh = 1/2 v2 ( as the mass is common )

9.8 . 3 = 0.5 v2

v2 = 58.7

v = 7.65 ms-1
 
 
 
 

Eg 2; A 4 kg stone is thrown from the top of a hill which is 20m high. It is thrown at 30 ms-1 at angle such that its maximum height reached is 15m.

a) How fast is it travelling at the top ?

b) How fast is travelling when it reaches the bottom ?


 
 

Soln; a) We could do this problem by the conventional projectile motion but because it only involves energy changes, that is a far simpler method.

The total energy of the stone at the start of the journey is composed of Kinetic Energy if we start by ignoring that it is above the sea.

Total Energy at start = Ek

= 1/2 mv2

= 0.5 . 4 . 900 = 1800 J

When it rises, 15m it loses kinetic energy but gains pot energy.

Ep gained = mgh' = 4 . 9.8 . 15 = 588 J

At the top we have a mixture of energies = starting energy

thus 1800 = 588 + new Ek

new Ek = 1800 - 588 = 1212 J = 1/2 m(vnew)2

thus vnew = 24.6 ms-1 = speed at the top.

b) At the bottom of the cliff, it has lost additional Ep which is converted into Ek

Additional Ek = mgh" = 4 . 9.8 . 20 = 784 J

new total energy is now = 1800 + 784 = 2584 J

This is now all kinetic energy, so 2584 = 1/2 m(vbottom)2

vbottom = 36 ms-1 near enough.

In every such operation, however, we usually lose some energy in undesirable forms, usually heat generated by friction or some such process.

Heat is not easily turned back into "useful" forms of energy. All of a car's petrol energy eventually turns into heat; much of in the first place out of the exhaust system, some into warming the surrounding air through drag, some in warming the oil in the various parts through friction and lastly in the brakes through friction.

Energy efficient buses try to avoid the latter loss by using some form of energy storage device for example a gyro ( storing kinetic energy ) or electrical generators for converting the vehicle's kinetic energy back to electrical energy.

Ironically, in our houses, we generate heat in stoves, hot water tanks and heaters from the Gravitational Pot. Energy of the stored water. Better insulation lessens the loss of such energy to the outside. Many other techniques exist for decreasing a home's reliance on Hydro energy. We pay, of course, for the Hydro energy we use. The electrical companies use a variant of the joule called a kilowatt-hour.

Most of our food energy is used to generate heat. This provides the conditions for our body cells to flourish in. Spare energy from this is available for doing our day-to-day activities and any left over goes into stored chemical energy called fat.

POWER

"Power is the rate of doing work or changing energy."

P = Work Done = ΔEnergy

                 t                                  t

A powerful person is capable of doing the same work as a less powerful person in a shorter time.

The unit of power is the watt, W which is the Js-1.

Eg ; If Poatina generates 500 MW at 90% efficiency from a head of water 1000m above the generator, how much water is needed each second ?

Soln; The water clearly loses Grav Pot Energy so that this is the energy change we need.

P = Work done = Δenergy
             t                        t

500 x 106 = mgh = m . 9.8 . 1000
                         t                 t

thus, m / t = 5.1 x 104 kg s-1 = 51 tonnes s-1

But the station is only 90% efficient, so the required amount of water is

= 51 x 100 / 90 = 56.7 tonnes s-1

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PROBLEMS

1. You push a table through 3m with a force of 30N. How much work have you done on the table? The table fails to accelerate continuously due to friction. What form of energy is created? ( 90 J)

2. In lifting a 20kg bucket of water through 2m from a hole, work has been done and energy transformed. What work have you done, where have you obtained the energy from and what form of energy has the water and bucket now got? (392J)

3. You are writing an English essay of total length 3 pages. Estimate how far the pen moves in your script and how much force you apply to the pen on average. Hence estimate how much work you do on the pen. Where does the physical (not mental! ) energy go that you expend? (Is there such a quantity as mental energy?) ( ~ 4J)

4. A major environmental push is for "energy conservation" in the house, work place etc. How does this conception differ from the pure physicists' conception of energy conservation?

5. Comets, in their highly elliptical orbits, travel fastest near the Sun and slowest out beyond Jupiter. Discuss the energy changes in such an orbit.