Unit III
Work, Energy, & Power

Work and Energy

Energy is defined as the ability to do work and work is done whenever there is a change or transfer of energy. Energy will produce work on an object if that object's displacement is changed.
Here's an example: A magnetic field surrounds a magnet, this is an energy field. A nail is put into this magnetic field. The nail moves in this field toward the magnet until it strikes the magnet. The magnetic field is said to have done work on the nail. The magnetic field produces a force that pulls the nail to itself. On being pulled toward the magnet the nail accelerates over a given distance. In summary, the magnetic field is the energy, producing a force that moves the nail. We can then say that work has been done on the nail since its displacement has changed.

Units for work and energy is the Joule or a Newton-meter

In order for work to occur three conditions must be met
Hence, no force no work and no displacement no work
It should be pointed out that you can have energy but no work, its only when the energy is being used that work is done.
The equation to calculate work is W = Fd. Both force and displacement are vectors however the product of the two is not. Work is a scalar

d can be used.

Graphical analysis of a force versus distance graph enable one to determine the work on that object by calculating the area under the curve. For straight line graphs this does not pose any difficulties. However a curved line will. (See page 150 )

Energy

Energy is defined as the ability to do work. Energy has several key characterists

  1. Energy is transfered from on object to another whenever work is done.
  2. Energy come in many forms and can be converted from one form to another. Here's a short list (see pages 154, 155, 156 of text)
    1. kinetic energy; the energy of motion
    2. gravity
    3. chemical
    4. magnetic
    5. nuclear
    6. electric
    7. heat or thermal
    8. sound
    9. light or radiant which comes in the form of electromagnticwaves. Remember the light unit where light is only a small portion of the electromagnetic spectrm
  3. Energy can be stored (potential) and used at later time to do work.
  4. Energy is always conserved in a closed system.
The units for energy is the same as work the Joule. However the joule is a rather small unit of energy measurement so the kilojoule or mega joule is used. Another important unit of energy is the kilowatt hour (kW.h) used for measuring electrical energy. Another unit used is the horsepower (HP) but this is a nonmetric unit and will probably not be used. Gasoline engines and electric motors are rated in HP.

Gravitational Potential Energy

Gravitational energy is the result of two objects being attracted to each other. Since one of the objects is usually the Earth, it becomes a constant in the equation. All objects are attracted downward. The heigher above the surface of the Earth, the greater the amount of work that can be done by gravity on that object. Since W = Fd the greater the value of "d" then the more work is done on the object. In the equation "F" will be a constant depending only on the mass of the object (F = ma where a = 9.8m/s2.
Note: symbol switch ===> "a" will be replaced with the letter "g". "d" will be replaced with the letter "h". "g" is for gravity and "h" is for height above the Earth. The force of gravity becomes FG = mg and the work done by gravity becomes
W = FGh or W = mgh.
For work to be done an object must change position or "fall".

Example to study
A book having a mass of 1.2 kg is on the floor. This would be the zero position. In order for it to be picked up and placed on the table energy must be applied. Lets say you are the energy source and you pick up the book. You do work on the book. If you know the height of the table you can calculate the workdone to place the book on the table. W = FGh. The height of the table is 0.92 m the the first step is to convert the mass of the object into the force FG. FG = mg or 1.2 x 9.8 = 11.76 or 11.8 N. The work done is W = FGh or 11.8 x 0.92 = 10.8 J or 11 J
Since 11 J or work was done on the book, when it is sitting on the table it now possess 11 J of Gravitational Potential Energy. Energy is never lost, it just gets transformed from one form to another. If a chair was under the table the book would have a relative gravitational potentail energy to the heigh of the chair. If the chair height was 0.5o m then the relative height difference is 0.92 - 0.50 = 0.42 m And the relative energy between the chair and the table would be a function of 0.42 m. Since EG = FGh the EG = 11 x 0.42 or 4.62 J. This is the energy difference between the chair and the table. If you subtract the two values you get the potential energy between the floor and the chair or 6.4 J (watch the round offs on the numbers)

Kinetic Energy

Kinetic energy is the energy of a body in motion. A body in motion must have had a force applied to overcome its initial inertia. The equation for kinetic energy is EK = 0.5mv2 . The derivation of this formula is found on page 163 so make sure you read it.
Do remember that energy and work are numerically the same so if you calculate one you get the other.

Energy Transformations

In the reaction of hydrogen gas and oxygen to produce water vapour the energy released is 258.4 kJ/mol of water vapour produced. When hydrogen and oxygen are mixed together they have the chemical potential energy to do work. If sealed in a metal tube with a cork on one end, upon reacting the cork will be propelled outward. the chemical energy would be transformed into kinetic energy of motion. Not all the energy would be transformed into energy of motion, heat, light , & sound are also produced. If 65% of the energy is transfered to the cork then the KE of the cork is 168 kJ.
If the cork has a mass of 56 g, what velocity can it attain?
KE = 168 000 J
m = 0.056 kg
V = "?" m/s , the unkown
Using the formula EK = 0.5mv2      v = 77.5 m/s (make sure you can do the arithmetic).

In the table example, the book falls off the table, what is the kinetic energy of the book as it just hits the floor ?
Data: m = 1.2 kg, a or g = 9.8 m/s2 d or h = 0.92 m and v1 = 0.00 m/s
Since kinetic energy cannot be directly found, the velocity as the book just hits the floor will be determined. The formula to use is #7, which gives a velocity of 4.25 m/s
Using the formula EK = 0.5mv2 and substituting KE = 11.8 J or 11 J. Notice, the same value as the potential energy.
This becomes an energy relationship between gravitational potential energy and the kinetic energy of a falling object. EG = KE or mgh = 0.5mv2. Do notice that the "m's" can be cancelled out.

Springs and pendulums will be dealt with in class in order to demonstrate experimentally the concept of conservation of energy. Here's an example of the energy conversions during the swing of a pendulum.

Machines, Power, & Energy

A machine is a device designed to make "work" easier or in some cases possible for a preson to do. If you have a flat tire you cannot lift your car, however using a car-jack enables you to raise the car and change the flat. Also, you cannot remove the wheel nuts without a tire wrench. These are examples of machines. Page 180 has pictures of 6 simple machines.
Some machines change one force into another, others transfer force from one place to another or cause an applied force to have its direction changed. Machines can amplify a force or decrease its size. You should and remember examples of each of these different machines.
One thing a machine cannot do: make energy. Machines change amplify but do not produce more energy than what can be inputed.

The Inclined Plane

The inclined plane is a simple machine that allows large objects to be lifted against the force of gravity,with less work than needed to directly lift the object.
An experiment will be done to confirm this concept. A mass will be lifted a given distance and the work calculated to do so. The same mass will be pulled up a ramp and the work required determined. The two values will be compared.
This leads to the concept of mechanical advantage. In each caes the amount of energy is the same, however the force or effort can be manipulated. This is what a machine does best.
Determining the efficiency of a machine, equations on page 181.

Levers and Pulleys

A lever consists of a rigid bar that can rotate about a fixed point called a fulcrum There are three classes of levers which depent on the position of the load to applied force to fulcrum. Page 183 has a picture of each type. Make sure you can define each.
Torque due to a force about an axis is a measure of the effectiveness of the force in producing rotation about that axis. It is defined to be the product of the force and the perpendicular distance from the axis of rotation to the application of the applied force or the load. This perpendicular distance is called the lever arm (l) . Torques has units of newton-meters but is not really considered to be work. The torque applied to one side of a lever must equal the torque on the other side of the lever. Since torque equals F x l, determing an applied force for a lever can be computed. Problems to be done in class.

Pulleys are another of the simple machines. Pulleys trade distance for effort so as to make lifting a heavy object easy that is, the applied force can be reduced. Pulley systems are found on the bottom of page 185. A simple lab activity is carried out, in which you build the pulley system and compare the effort force to the load and the distance the load is raised to the distance pulled by the effort. Machanical advantage can then be determined.

Power

Power is defined as the rate of doing work. The faster the work is done the more power either developed or used. Power is not energy. The energy required to do a job is a fixed quantity, however the power employed to complete the job can be varied. The units for power is the watt
Here's a simple example. There are 100 4.0 kg bricks in the parking lot and they have to be brought into the class room. The FG per brick is 39.2 N with a total energy required of 3.92 kN. If the height from the parking lot to the class room is 30.0 m the energy needed to lift all the bricks is 117.6 kJ of energy. Now here's were power comes in. How long would it take you to carry all those bricks up the stairs? Lets say 1/2 hour or 1800 s. The power required is 65.3 W. However suppose you load all the bricks onto two carts and push them onto an elevator and the job is done in 5.0 minutes or 300 seconds. What's the power now? 117.6 kN / 300 = 392 W. Notice the big difference in power; but the work done is still the same. The faster a job is done the more power is used.

Thermal Energy: Heat

Thermal energy is the sum of the potential energy and kinetic energy possessed by the molecules of an object. This energy is exhibited by the various modes of motion of the molecules that make up the substance. There are three factors that effect this amount of energy.

  1. Mass of the material
  2. Temerature of the material
  3. Type of material, molecular composition of the material

Heat is the thermal energy being absorbed, released, or transfered from on object to another.

Problems where done in class. For more solved examples
Experiment done in class to determine the specific heat of a metal.

Harnessing energy sources is generally the process of generating and using electricity. Resources of energy come in two forms:renewable and nonrenewable. The terms should be obvious in meaning. The text defines nonrenewable as energy sources that are used up faster than it can be replaced. Some texts will say that a nonrenewable energy is one that once used cannot be replaced. Renewable energy can be replaced or may be viewed as always there; such as sunlight or wind power. A water fall such as Niagara, producing electricity, is considered to be renewable.
See section 5.4 in the text book for hydro electric diagrams.