# Work energy and Power

## Work energy and Power

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# Work energy and Power

Work is defined as the product of Force × Displacement.

# W = F × d

Work = Force x Displacement*

The unit of work is the Joule (J).

Energy is the ability to do work.
The amount of energy something has is also the amount of work it can do.
Because work is a form of energy it follows that the unit of energy is also the Joule.

Different Forms of Energy
Kinetic Energy is energy an object has due to its motion.

EK  = ½ mv2 *

Formula for Kinetic Energy:

Potential Energy is the energy an object has due to its position in a force field.

EP = mgh

The formula for Potential Energy:

Any time work is done energy is transferred*
Go through problem 7, page 128 carefully and try to understand what’s going on – this concept comes up in many different areas in physics.

The Principle of Conservation of Energy*
states that energy cannot be created or destroyed but can only be converted from one form to another.

Loss in Potential Energy  = Gain in Kinetic Energy for a freely falling object*

The Solar Constant is the average amount of the Sun’s energy falling normally on one metre squared of the Earth’s atmosphere per second.

Collisions:  Kinetic Energy and Momentum
When two objects collide, momentum is conserved provided no external forces act on the system.
Kinetic energy however is not conserved.
This is because some of the kinetic energy gets converted to sound and heat energy.

This is a common exam question.

### PowerPower is the rate at which work is done.Or Power is the rate at which energy is converted from one form to another.

The unit of power is the Watt (W).

To Estimate the Power developed by a person running up a flight of stairs.

• Time how long it takes to run up a flight of stairs.
• Calculate the work done in going up the stairs.

This will be the same as your potential energy at the top (mgh), where m is your mass.

• Divide the work by the time taken.

A similar approach could be used to calculate the power developed by a person repeatedly lifting weights.

Percentage Efficiency
No machine is 100% efficient – some energy is always ‘lost’ in the process.
This is why we can never have a ‘Perpetual Motion’ machine.

Formula to calculate how efficient a machine is:

Leaving Cert Physics Syllabus

 Content Depth of Treatment Activities STS 1. Work Definition and unit. Simple experiments. Appropriate calculations involving force and displacement in the same direction only. Lifts, escalators. 2. Energy Energy as the ability to do work. Different forms of energy. Ep = mgh               Ek = ½ mv2 Conversions of one form of energy to another. Principle of conservation of energy. Demonstration of different energy conversions. Appropriate calculations. Sources of energy: renewable and non-renewable.   Efficient use of energy in the home. Solar constant (also called solar irradiance). 3. Power Power as the rate of doing work or Rate of energy conversion. Unit Estimation of average power developed by Person running upstairs Person repeatedly lifting weights etc. . Appropriate calculations Power of devices, e.g. light bulbs, motors, etc.

Extra Credit
*Work = Force ×  Displacement
So if eight forwards try to push a scrum machine for five minutes without it actually moving then in scientific terms they are not doing any work.
Alternatively, if another set of forwards manage to push the machine around the pitch and finish up back where they started, then unfortunately they too would be considered to have done no work. Why not?
Also, the Force and Displacement must be in the same direction; if they are not they you have calculate and use  the component of the force which is in the same direction as the displacement.

* E = ½ mv2
This means that the Energy a car has (and therefore its driver) is proportional to the square of the velocity.
If your speed increases by a factor of two (say from 20 mph to 40 mph), the energy increases by a factor of four.
If your speed increases by a factor of three (say from 20 mph to 60 mph), the energy increases by a factor of nine!

*Anytime work is done energy is transferred
This is a very important concept but is often overlooked by students. We will come across it again when dealing with an electron getting accelerated between two points. By which time you will all have forgotten about this.
When a body does work it loses energy.
For example if you carry a block upstairs, you do work and the chemical energy in your muscles decreases.
If work is done on an object it gains energy.
The block gains energy as it moves up.

*The Principle of Conservation of Energy
This means that all the energy all around us could only have come from the Big Bang 15 billion years ago – imagine that!
Every sound you hear, every movement you make, all that energy originally came from something the size of a pin-head. Personally I think that’s mind-blowing.
If you don’t then maybe it’s not too late to give up Physics and switch to Accounting.
Now while this energy can’t disappear (you can’t actually waste energy), it can only change form.
This is what an Energy Conversion is.
Energy conversions are going on all around us all the time.
The table on page 127 gives some examples.
The problem with these energy conversions is that either they are taking a less useful form (lightbulb giving out heat) or the useful energy going out is less than the energy taken in (power stations).
The technical term is that the energy is ‘less ordered’, or ‘more chaotic’.

*Loss in Potential Energy  = Gain in Kinetic Energy for a freely falling object
This means that the total energy of the object is the same at any point in its trajectory (‘freely falling’ means no external forces).
Note that when an object is thrown up the opposite holds, i.e. gain in potential energy = loss in kinetic energy.
You could check this for yourself by looking at a mass of say 10 kg, thrown up with an initial velocity of 100 m/s.
Find how far up it goes (how? – hint; use equations of motion), and then find its potential and kinetic energies at the bottom, half way up and at the top.
In each case they will have the same total (potential + kinetic) at each point.
A couple of very important problems are shown on page 129; Problems 10, 11 and 12.

There is something else worth noting in problem 12;
To find the velocity of the object at the bottom we noted that potential energy at the top equals kinetic energy at the bottom, i.e. mgh = ½ mv2, but we could also have used equations of motion,
i.e. v2 = u2 +2as, and that too would have given us the velocity.
Therefore the velocity a pendulum has at the bottom of a swing is the same as that which it would have if it were falling straight down (freefall)!

When two balls go in, two go out at (almost) the same speed: Momentum is conserved, although Kinetic Energy is not.
So why, if two go in, can't one go out at twice the velocity?
Turns out momentum would be conserved, but Kinetic Energy wouldn't.
Try working it out by letting the mass of each sphere be  m, and the initial velocity be v.

Exam Questions

## Work

• [2007 OL]

Define work and give the unit of measurement.

• [2006 OL]

A person pushed a car a distance of 15 m with a force of 500 N. Calculate the work done by the person.

• [2002 OL]

The force T exerted by the engine in an aircraft is 20 000 N. Calculate the work done by the engines while the aircraft travels a distance of 500 km.

## Energy

• [2005 OL]

Define energy.

• [2009 OL]

Which of the following is the unit of energy; kilogram, watt, joule, ampere?

• [2008][2005]

State the principle of conservation of energy.

• [2010 OL]

Define kinetic energy

• [2005 OL]

Name one method of producing electricity.

• [2005 OL]

What type of energy is associated with wind, waves and moving water?

• [2007 OL]

Which of the following is not a renewable source of energy: wind, nuclear, solar, hydroelectric?

• [2005 OL]

Give one disadvantage of non-renewable energy sources.

• [2005 OL]

How does the sun produce heat and light?

• [2003 OL]

State one energy conversion that takes place in an electrical generator.

• [2005 OL]

What energy conversion takes place when a fuel is burnt?

• [2004 OL]

What energy conversion takes place in a solar panel?

• [2008]

Why is a fluorescent tube an efficient source of light?

• [2007]

Why is a filament light bulb not an efficient source of light?

• [2007 OL]

What is the difference between potential energy and kinetic energy?

• [2005 OL]

Give one factor on which the potential energy of a body depends.

## Energy: Maths questions

• [2004 OL]

A student holds a metal ball 2 m above the ground. The mass of the ball is 5 kg.
Calculate the potential energy of the ball.

• [2002 OL]

A car of mass 800 kg is travelling at 10 m s-1. What is its kinetic energy?

• [2009 OL]

A train of mass 30000 kg can reached a top speed of 50 m s−1.
As the train approached the next station the driver applied the brakes uniformly to bring the train to a stop.

• Calculate the kinetic energy lost by the train in stopping.
• What happened to the kinetic energy lost by the train?
• [2010 OL]
• An ice skater of mass 50 kg was moving with a speed of 6 m s−1 then she collides with another skater of mass 70 kg who was standing still. The two skaters then moved off together at a speed of 2.5 m s−1.

Calculate the kinetic energy of each skater before the collision.

• Calculate the kinetic energy of the pair of skaters after the collision.
• Comment on the total kinetic energy values before and after the collision.
• [2008]

In a pole-vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints from rest and reaches a maximum velocity of 9.2 ms–1.
What is the maximum height above the ground that the athlete can raise his centre of gravity?

• [2004]

A pendulum bob was raised to a height of 20 cm and allowed to swing so that it collided with a block at rest on a bench, as shown.
Calculate the velocity of the bob just before the collision.

• [2005]

A basketball of mass 600 g which was resting on a hoop falls to the ground 3.05 m below.

• What is the maximum kinetic energy of the ball as it falls?
• On bouncing from the ground the ball loses 6 joules of energy.

What happens to the energy lost by the ball?

• Calculate the height of the first bounce of the ball.

## Power

• [2002][2006][2007 OL]

Define power.

• [2005 OL][2007 OL]

What is the unit of power?

• [2008]

A toaster has a power rating of 1050 W when it is connected to the mains supply.
Calculate the heat generated by the toaster in 2 minutes if it has an efficiency of 96%.

• [2002 OL]

A kettle uses 532 950 J to boil water. If it takes 4 minutes calculate the power of the kettle.

• [2006 OL]

During a ten-hour period the energy gained by the bricks in a storage heater is 34.2 MJ.
Calculate the power of the heating coil.

• [2007 OL]

An empty lift has a weight of 7200 N and is powered by an electric motor. The lift takes a person up 25 m in 40 seconds. The person weighs 800 N.

• Calculate the total weight raised by the lift’s motor.
• Calculate the work done by the lift’s motor.
• Calculate the power output of the motor.
• Calculate the energy gained by the person in taking the lift.
• If instead the person climbed the stairs to the same height in 2 minutes, calculate the power generated by the person in climbing the stairs.
• Give two disadvantages of using a lift.
•  [2003]

A person in a wheelchair is moving up a ramp. The force required to keep the wheelchair moving at a constant speed up the ramp is 156.3 N. The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her 10 s to travel up the ramp.

The Solar Constant

• [2007]

A large number of solar cells are joined together in series and cover an area of 20 m2.
The efficiency of the solar cells is 20%. If the solar constant is 1400 W m–2, what is the maximum power generated by the solar cells?

• [2002]

The solar constant is 1.35 kW m-2. What is the average amount of energy falling normally on each square metre of the earth’s atmosphere in one year? (one year = 3.16 × 10 7s)

• [2009]

What is the max energy that can fall on an area of 8 m2 in one hour if the solar constant is 1350 W m–2?

• [2006]

The average value for the solar constant in Ireland is 1.2 × 102 W m–2. What is the average energy falling normally on an area of 5 m2 of ground in Ireland in 1 minute?

• [2007]

Nuclear power generates three hundred gigawatts of energy worldwide.
How much energy is generated worldwide every minute by nuclear power today?

• [2008 OL]
• State two uses of energy in the home.
• Give two ways to reduce energy needs in the home.
• List the main sources of renewable energy.
• What are the main parts of a solar heating system?
• Why does a solar panel need to face south?
• What is the function of the backup heater?
• Why are parts of the solar panel painted black?
• What is the name given to the tendency of water to circulate as it is heated?

Exam Solutions

## Work

• Work is the product of force by displacement (distance).

Unit: joule

• Work = Force × distance = 500 × 15 = 7,500 J.
• Work = Force × displacement       Þ 20000 × 500 000 = 1 × 1010 (J)

## Energy

• Energy is defined as the ability to do work.
• The joule
• The Principle of Conservation of Energy states that energy cannot be created or destroyed but can only be converted from one form to another.
• Kinetic energy is energy an object has due to its motion.
• Solar, wind, wave, tidal, biomass, coal, oil, gas, hydroelectricity, geothermal, nuclear, uranium, turf.
• Renewable energy.
• Nuclear
• They will run out.
• Through nuclear reactions.
• Kinetic to electric.
• Chemical to heat.
• Light to electricity, light to heat.
• Most of the (electrical) energy is converted to light (energy)
• Almost all of the energy is given off as heat.
• Potential energy is energy a body has due to its position; kinetic energy is energy a body has due to its motion.
• Mass, height, acceleration due to gravity (g).Energy: Maths questions
• Ep = mgh = 5 × 9.8 × 2 = 98 J.
• Ek = ½mv2             Þ E = ½ 800 × 102     Þ E = 40,000 J
•
• Ek = ½mv2

Ek = ½ (30000)(50)2 = 37500000 J = 37.5 MJ

• It was converted to other forms of energy such as heat, sound and light (from sparks).
•
• Ek = ½mv2

Ek = ½ 50 × 62 = 900 J
Ek = ½ 70 × 0 = 0 J

• Ek = ½ 120 × (2.5)2 = 375 (J)
• Kinetic energy not conserved in collision because some of the energy was given off as heat and sound.
• K.E. = P.E.

½ mv2 = mgh
h = v2/2g    = (9.2)2/2(9.8) = 4.32
Max height above the ground = 4.32 + 1.1 = 5.42 m.

• Loss in P.E = gain in K.E

mgh = ½ mv2
v2 = 2gh = 2(9.8)(0.2)
Þ v = 1.98 m s-1

•
• KE = PE (at height of 3.05 m)

½mv2 = mgh
mgh = (0.6)(9.8)(3.05) = 17.9 J
Ek  = 17.9 J

• It changes into sound and heat.
• [retained energy = 17.9 – 6]   Þ  E = 11.9 J

E = mgh     Þ  h = E / mg    Þ h = 11.9 /(0.600)(9.8)       Þ       h = 2.02 m
Power

• Power is the rate at which work is done.
• The watt.
• Heat generated = power × time

Heat = 1050 × 120 = 1.26 × 105 J
96%  = 1.21 × 105 J

• P=W/t        Þ P = 532 950/240     Þ P = 2221 W.
• P = W/ t     Þ        P = 34 200 000 / (10×60×60) = 950 W
•
• 7200 + 800 =  8000 (N)
• Work = Force × distance = 8000 × 25 =  200,000  J (200 kJ)
• Power = work/time =200,000/40 = 5000 W
• Energy = Force × distance = 800 × 25 = 20,000 J
• Power = work/time = (800 × 25)/120 = 166.6 W
• Needs more energy / uses energy / no exercise so not good for health /cost involved / can be dangerous, etc.
• Power  = work/time

Work = Force × displacement = 156.3 × 5 = 780 J
Power = 780/10 = 78 W

The Solar Constant

• (1400 × 20 × 1/5) W or 5600 J s-1 or 5600 W
• Solar constant by time = (1.35 × 103)(3.16 × 107)  =        4.27 ×1010J
• 1350 × 8 × 3600

Emax = 3.9 × 107 J

• (Note that the solar constant for Ireland is less than 10% of what it is for the planet Earth as a whole.)

Energy per minute on 5 m2 = (1.2 × 102)(5)(60) = 36,000 J or 3.60 x 104 J

• (300 x 109)(60) J or 18,000 gigajoule (per minute) or 1.8 x 1013 J
•
• Heating, cooking, lighting, TV etc
• Insulate, double glaze, reduce usage, use low energy appliances, turn off unused lights, etc.
• Solar, wind, wave, tidal, geothermal, biomass
• Solar panel, hot water storage cylinder.
• To get the most sunlight.
• For use at night or in poor sunlight.
• Black is a good absorber of heat
• Convection

Source : http://www.thephysicsteacher.ie/LC%20Physics/Student%20Notes/11.%20Work,%20Energy%20and%20Power.doc

Author : not indicated on the source document of the above text

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