# Work, Energy and Power

The Basics

### What is Work?

In classical physics terms, you do work on an object when you exert a force on the object causing it to move some distance. The amount of work you actually do may have little relationship to the amount of effort you apply. For example, if you push on a car stuck in a snow drift, you may exert a lot of force (and effort) but if the car does not budge, you have not done any work! In order for work to be done on an object, the object must move some distance as a result of the force you apply. There are also constraints on the force you apply. Only force exerted in the same direction as the movement of the object result in work. You may think that you do a lot of work if you carry an arm full of books from home to school. In reality you do no work at all! In carrying the stack of books, you exert an upward force to hold the books so they don't fall to the ground. There is no movement associated with this force. As you walk, the motion of the books is horizontal not vertical. Since the force applied to the books is vertical, and the motion is horizontal, you do not do any work on the books.

Work is a transfer of energy so work is done on an object when you transfer energy to that object. The amount of work done on an object depends on the amount of force exerted on the object and the amount of distance the object moves.

Work = Force x Distance

According to Newton's Second Law of Motion, the net force on an object is dependent on the mass of the object, and its acceleration during the movement.

Force = Mass x Acceleration

The common unit of force is the Newton (N). One Newton is the force required to accelerate one kilogram of mass at 1 meter per second per second.

1 N = 1kg m/s2

The amount of work done to push a 10,000 N car a distance of 10 meters would be

10,000 N x 10 m = 100,000 N m or 100,000 J

The Newton-meters are termed joules (J). The joule is named after James Prescott Joule (1818-1889) who first calculated the amount of electrical work needed to produce a unit of heat. In his experiments, Joule discovered that the same amount of heat was produced by the same amount of either electrical or mechanical work ("the mechanical equivalent of heat").

### What is Energy?

On March 10, 2005 sounding like an approaching locomotive, a tornado dropped out of billowing black clouds on the New Zealand town of Greymouth. The winds hurled a truck into a lagoon, snapped power poles in half, roofs sailed through the air and buildings were destroyed (go here to see a video of this disaster).

Although wind is just moving air, it possesses energy. When the wind moves the leaf on a tree or picks up and hurls a truck, it has caused a change in the position of the object. Therefore it has done work. A measure of the ability to do work or cause change is called energy. Any time an object does work on another object, some of the energy of the working object is transferred to that object raising its energy state. Like work, the units of energy are joules.

Energy is the amount of work a physical system is capable of performing so energy can be defined as that which changes the position, physical composition or temperature of an object. There are two categories of energy, kinetic energy and potential energy. The difference between them is whether the energy is being transferred (kinetic) or stored (potential). They are interconvertible.

Kinetic energy is the energy of motion (the motion of waves, electrons, atoms, molecules) while potential energy is stored energy or energy of position that has the potential to do work (follow the kinetic and potential energy links for a more in depth discussion). The kinetic energy of an object is dependent both the mass of the object and its velocity.

K.E. = 1/2 m v2

Thus a 3,000 lb car moving at 50 mph will transfer more kinetic energy than a 2,000 lb car moving at the same rate. Energy can be stored in an object by lifting it up. The amount of potential energy would be

P.E. = mgh

where m is the mass of the object; h is the height of the object, and g is the force of gravity acting on the object.

This animation shows how energy converts between kinetic and potential energy.

Animation courtesy of: http://www.bsharp.org/physics/stuff/swings.html

View how kinetic and potential energy are interrelated using a roller coaster demonstration.

A waterfall possesses both potential and kinetic energy. The water at the top of the falls possesses potential energy. As the water flows over the edge of the falls, its energy is changed into kinetic energy.

### Forms of Energy

Both potential and kinetic energy come in a variety of forms.

 Energy Form Description Examples Mechanical Energy The energy associated with the motion or position of an object. This can occur as either kinetic or potential energy. Read this article on mechanical energy. pushing a car Chemical Energy Potential energy stored in the bonds that hold the atoms together in a molecule fossil fuels, food energy Thermal Energy The internal energy of substances caused by vibration and movement of atoms and molecules within the substance. hot water, steam Electrical Energy The energy of moving electrical charges. batteries, lightening Radiant Energy Electromagnetic energy that travels in waves which possess both electrical and magnetic properties. Visible light, ultraviolet, infrared, radiowaves and microwave radiation are all examples. sunlight Nuclear Energy Potential energy stored in the nucleus of an atom. Nucleus of a uranium atom Gravitational Energy Energy of place or position. Water held behind a dam is an example of gravitational potential energy. When the water is released, its energy becomes mechanical energy. Hydroelectric reservoir

### The Law of Conservation of Energy

Within a system the amount of energy is constant. Energy can be neither created nor destroyed. However, It can be transferred from one form to another. Thu, when the water at the top of the waterfall plunges over the edge, potential energy is converted to kinetic energy. The energy of an air molecule moving in wind can be converted to rotational energy when moving the rotor of a windmill which then can be converted into electricity by a wind turbine generator. In almost all of these processes some energy is also converted into heat energy.

### Units of Energy

Since we use energy to do many different types of work such as electrical, mechanical and thermal work, there are many different units used to measure the quantities of energy used. For example, the joule is a measure of electrical energy while the calorie or British thermal unit (BTU) is typically used for measuring thermal energy.

 Some Common Energy Units joule (J) The amount of work or energy exerted when a force of one newton causes a displacement of one meter also the energy needed to maintain a flow of 1 ampere for 1 second at a potential of 1 volt in electrical applications calorie (cal) The energy needed to raise the temperature of 1 gram of water by 1 oC 1 cal = 4.184 J the nutritional Calorie is in actuality a kilocalorie (kcal) 1 C = 1 kcal = 4.184 J British Thermal Unit (BTU) The energy needed to raise the temperature of 1 pound of water by 1 oF 1 BTU = 1055 J the unit used extensively in engineering applications heating and cooling units (air conditioners) are rated in BTU units

The following factors can be used to convert among these energy units:

1 J = 0.2388 cal
1 cal = 4.1868 J
1 BTU = 1.055 kJ = 0.252 kcal

 Interesting Fact A 2.1 oz. Snickers bar contains 280 Calories. In normal energy terms, this is 280,000 cal or 280 kcal. The amount of energy in a Snickers bar is capable of raising 280 kg of water 1 oC. This amount of energy is capable of raising the body temperature of a 70 Kg (154 lb) person by 4 oC.

To compare the energy that can be extracted from various fuel sources, we need to be able to equate the standard unit of measurement, the joule, to the units commonly used with various fuels such as gallons of gasoline, cubic feet of natural gas and metric tons of coal. The following table shows some of these energy equivalences.

### Energy EquivalencesTaken from: Craig, Vaughan, Skinner, Resources of the Earth, 3rd Ed. Prentice Hall

1 milllion (106) BTU equals approximately:

90 lbs of butuminous coal and lignite production
125 lbs of oven-dried wood
8 gallons of gasoline (enought to move an average passengar car ~124 miles)
10 therms of dry natural gas
11 gallons of propane
2 months of dietary intake of a laborer
20 cases (240 cases) of table wine

Here are some other useful energy equivalents and conversion factors that will be useful in comparing the energy content of different fuel sources:

WEC (World Energy Council) Standard Energy Units
1 tonne of oil equivalent (toe) = 42 GJ* (net calorific value) = 10 034 Mcal
1 tonne of coal equivalent (tce) = 29.3 GJ (net calorific value) = 7 000 Mcal

*NOTE: GJ (gigajoule)= 109 J

Volumetric Equivalents
1 barrel = 42 US gallons = 158.9 liters = 0.1589 m3
1 cubic meter = 35.315 cubic feet = 6.2898 barrels

Representative Average Conversion Factors
1 tonne of crude oil = approx. 7.3 barrels
1 tonne of natural gas liquids = 45 GJ (net calorific value)
1 000 standard cubic metres of natural gas = 36 GJ (net calorific value)
1 tonne of uranium
(light-water reactors, open cycle) = 10, 000 – 16, 000 toe
1 tonne of peat = 0.2275 toe
1 tonne of fuelwood = 0.3215 toe
1 kWh (primary energy equivalent) = 9.36 MJ = approx. 2 236 Mcal
1 Therm of natural gas = 100,000 BTU

A handy calculator for converting between energy units can be accessed here. You can download an Excel unit converting spreadsheet or use this energy conversion table .

 EXAMPLE In order to compare two different energy sources, you should convert them both to the same energy unit. Suppose you use natural gas as your home heating fuel while your brother uses heating oil to heat similar 2,000 sq ft. houses. You consume 80,000 cubic feet of natural gas, and your brother uses 500 gallons of heating oil during the winter. Which of you has used more energy to heat your house? Conversion Factors: 1 gal heating oil = 139,000 BTU 1 cubic ft natural gas = 1, 026 BTU Solution: # BTU Natural Gas Used = (80,000 ft3) (1,026 BTU/3) = 82,080,000 or 8.2 x 107 BTU # BTU Heating Oil Used = (500 gal) (139,000 BTU/gal) = 69,500,000 or 6.9 x 107 BTU You used more energy to heat your house.

 PROBLEM You are an executive for the local power company. The company's power generators will run on either natural gas or residual fuel oil. It is your job to switch the generators between the two fuels so that you are always using the less expensive fuel to keep costs down. Your generators are currently running on natural gas but the price of natural gas is rising more rapidly than the price of residual fuel oil. Based on the fact that natural gas costs \$4.87 per thousand cubic feet and residual fuel oil costs \$28.30 per barrel, determine if you should switch to residual fuel oil or remain on natural gas. (To check your answer, place your mouse over Mozilla.) 1 cubic foot of natural gas = 1,026 BTU 1 barrel of residual fuel oil = 6,287,000 BTU

### What is Power?

Energy is a measure of how much work can be done without any consideration of how long it takes to accomplish the work. Power is the measure of how quickly the work is done so it is a time-dependent function. Thus, two marathon runners do the same amount of work when they run the 26 miles, 385 yards or 42 kilometers. However, the runner that finishes the marathon in 2 hours 30 minutes runs twice as powerfully as the runner that finishes in 5 hours. Power is the amount of energy used per unit of time. The difference between energy and power is that power may be measured at any point in time, while energy has to be measured during a certain time period such as a second or an hour.

Power = Work/Time = (Force x Distance)/time

### Units of Power

The unit of power is joules per second or J/s when work is measured in joules and time in seconds. The basic unit of power, 1 J/s is called a watt (W), named after James Watt who made important improvements to the steam engine. By definition, a watt is the consumption of one joule of energy per second.

1 W = 1 J/s

 PROBLEM A crane lifts an 8,000-N beam 75 meters to the top of a building in 30 seconds. How much power does the crane use? (To check your answer, place your mouse over Mozilla.)

If work is the transfer of energy, power is the rate at which energy is being transferred from one object to another or converted from one form into another. Light bulbs are rated by their wattage output. The power of a light bulb, its wattage, is the rate at which the bulb converts electrical energy into radiant light and thermal energy. A 100 W light bulb is brighter than a 60 W light bulb because it converts 100 joules of electrical energy per second while a 60 W light bulb converts 60 joules every second.

The watt is a relatively small amount of power. You produce about 1 W of power raising a glass of water to your mouth over a one second time period. Since the watt is such a small unit, power is often measured in kilowatts (KW). When describing the power of engines, the power unit used is often the horsepower. To promote his steam engines, James Watt compared the amount of work an engine could do to the common power source of the late 1700s, the horse. One horsepower (hp) was defined as the amount of work a horse does to lift a 33,000 pound weight a distance of one foot in one minute. This may seem like an odd definition, but it was based on the work a horse did hauling coal (Watt was trying to encourage the use of steam engines in coal mining).

1 hp = 33,000 foot-pounds (ft/lb)/min

A horse moving 33,000 pounds of coal a distance of one foot; one moving 330 pounds a distance of 100 feet; or another moving 33 pounds 1,000 feet in a minute are all exerting the same power.

The term horsepower implies the amount of muscle a particular engine has while energy tells how much "work" the engine performs during a given period of time.

 Power Units Watt (W) the power resulting from an energy dissipation, conversion, or storage process equivalent to one joule per second 1 KW = 1000 W = 1000J/s The megawatt (MW) is the unit by which power generating plants are often rated 1 MW = 1,000,000 W Horsepower (hp) a unit of power representing the power exerted by a horse in pulling 1 hp= 746 W Used to express power in mechanical energy expenditure.

 PROBLEM Consider taking a 1-horsepower horse and putting it on a treadmill to operate a generator. How many watts of energy would the horse continuously generate? If the energy output of the generator was run through a electric heater, how many BTU would be produced in an hour?. Since the BTU is equal to 1,055 joules or 0.252 food Calories. How many Calories would this horse burn in one hour if it were 100-percent efficient? To check your answers, place your mouse over Mozilla.

The kilowatt-hour (kWh) is a commercial unit of electrical energy. It is the amount of energy that results from the steady production or consumption of one kilowatt of power over one hour. It is equivalent to 3.6 megajoules of energy or 3412 BTU. Although this is not a standard measurement unit for any scientific system, it is the unit by which electrical consumption in homes and businesses is measured.