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Old Saturday, October 04, 2008
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Default Work and Energy

Work is a Result of Force


Work is defined in as the result of applying a force to an object to move it a certain distance. Since objects tend to continue moving after a force is applied, the distance is only measured while that force is being applied. When the force is used to change the velocity of the object, the work is against inertia. the work can also be done against a resistive force.

Questions you may have include:
  • What is the relationship of work to force?
  • What is work against inertia?
  • What is work against a resistive force?

Work is force times distance
The definition of work is that it equals force times the distance traveled while that force is being applied or

W = Fd

where:

W is the work in joules (J or kg-m/s) or foot-pounds
F is the force applied to an object in newtons (N or kg-m/s) or pounds (lbs)
d is the distance the object moves in meters (m) or feet (ft)
Fd is F times d

Note: W indicates work. Sometimes W is also listed as weight. We will use the small w for weight, but still, you should always make sure you read the definition below the equation to make sure you understand what the letters stand for.

If you would apply a force of 2 newtons to move an object 3 meters, the work done would be 6 joules.

If a force is applied on an object and there is no movement, then there is no work. If you push on a heavy object but are unable to move it, you are making an effort but you are not doing any work, according to the scientific definition of work.

Work against inertia
When you apply a force on a stationary but freely moving object, you are working against its inertia or tendency to remain stationary. This also applies to changing the velocity or direction of an object. The work done on a freely moving object only occurs over the distance while you are applying the force.

Examples
For example, if you throw a ball, the work done consists of the distance you accelerated the ball until you let it go. Once you have thrown the ball, it will continue at a constant velocity (minus the effect of air resistance) and no further work is done.

Another example of work against inertia is the work done by the force of gravity, when you drop an object from some height. Since the force of gravity is F = mg, where m is the mass of the object and g is the acceleration of gravity, the work done in dropping an object from a height h is W = Fd = mgh.

Note that the equation W = mgh is the same as for the potential energy of an object at some given height: PE = mgh. (See Potential Energy for more information.)

Carrying a heavy box
If you are holding a heavy box and carry it across the room, the work you are doing against inertia is the force you apply to move the box (F = ma) times the distance you carry it.

Note that many textbooks say that this is not work, because the force of gravity is perpendicular to your motion. Unfortunately, they are unclear about the type of work they are talking about. Moving the box across the room is work against the inertia of the box, while lifting the box up is work against the resistive force of gravity.

Work against a resistive force
A resistive force is a force that causes a moving object to slow down or tends to prevent a stationary object to move. The resistive force acts in a direction opposite to the one that you want to move the object. Just as going against inertia, the distance is only measured while the force is applied, since it is possible for an object to continue moving a short distance after the force is released, even though it is moving against a resistive force.

Work against gravity
When you lift a heavy object, you are doing work against the force of gravity. The force required to life the object is its weight

F = mg

where

F is the force required to lift the object and is its weight
m is the mass of the object
g is the acceleration due to the force of gravity (9.8 m/s or 32 ft/s)

The amount of work you must do is the weight of the object times the height you are lifting it. Thus W = mgh, where h is the height you are lifting it. The amount of work you do to lift an object of mass m to a height h is the same amount of work done by gravity if you drop the object from that height.

Work against friction
Friction is a force of resistance to anything that is moving or sliding along a surface or material. For example, if you push an object along the floor, the force of friction provides the resistance to the motion. If you slide the object a certain distance along the floor, the work done is

W = Frd

where:

W is the work done
Fr is the resistive force of friction
d is the distance you slid the object


If you pushed an object across a slippery floor, it might continue to slide for a short distance after you stopped pushing. Your work would be measured only for the distance you pushed the object.

Summary
Work is the result of a force moving an object a distance, measured while that force is being applied. The equation for work is W = Fd. Work can be to overcome inertia, as well as to work against a resistive force. Gravity can do work against inertia and you may do work against the force of gravity.




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  #2  
Old Saturday, October 04, 2008
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Types of Energy


Energy is defined as the capacity to do work. When a force applied on an object moves that object, work is done and energy is expended. An object has kinetic energy if it is moving. If there are some constrained or pent-up forces, preventing the object to move, the object is said to have potential energy. There are various subsets or forms of both kinetic and potential energy.

Questions you may have include:
  • What is kinetic energy?
  • What is potential energy?
  • What are subsets of kinetic and potential energy?


Kinetic energy
The standard textbook definition of energy is the "ability to do work." Unfortunately, this definition does not really give a good picture of what energy is all about. We normally think of an object having energy as one that is moving. The energy of a moving object is called kinetic energy and is abbreviated as KE.

The properties of kinetic energy are that the greater the mass of a moving object, the greater its energy will be. Also, the faster it goes, the greater its energy. That energy is proportional to the square of the velocity.

The equation for calculating the kinetic energy of an object is

KE = mv

where:

m is the mass of the object
v is its speed of velocity and v is the velocity squared or v times v
mv is one-half times m times v
Note that the velocity of the object must be much less than the speed of light. When the speed of an objectsuch as an atomic particleapproaches the speed of light (c), its kinetic energy approaches E = mc, according to the Theory of Relativity.

Potential Energy
There are situations when an object has the potential to start moving and gain kinetic energy. Often there are forces acting on the object, but the forces aren't yet sufficient to move the object.

Potential due to gravity
If you hold an object a distance from the floor, it has the potential to start moving, once you let it go. The force of gravity is pulling on the object, giving it potential energy. The equation is

PE = mgh

where:

PE is the potential energy
m is its mass
g is the acceleration of gravity (32 ft/s or 9.8 m/s)
mg is the weight of the object (m times g)
h is the height of the object from the floor or ground
PE becomes KE
If you drop the object, its potential energy will become the kinetic energy of motion (PE = KE).

Since PE = mgh and KE = mv, then:

mgh = mv

You can determine the speed it will be traveling after falling a height h by solving the equation for v:

v = 2gh

Take the square root of both sides of the equation:

v = SQRT(2gh) or v = √(2gh)

Note that the mass m cancels out of the equation, meaning that all objects fall at the same rate.

Thus, if h = 1 ft, and since g = 32 ft/s, then v = 2*32*1 = 64 and v = √64 = 8 ft/s.

Other types of PE

Other examples of potential energy that could cause motion include explosive chemical compounds and a coiled spring, ready to be released. A stretched rubber band, also has potential energy.

With chemical explosives, it is difficult to calculate the potential energy without experimenting to see how much kinetic energy is released in an explosion.

With a compressed spring, there are calculations that can determine its strength and potential energy.

Other forms or subsets of energy
Often, you will hear about other forms of energy, such as heat and electrical energy. In reality, they are also kinetic energy.

Heat energy
Heat is the movement of molecules. It is the sum of the kinetic energy of an object's molecules. In many physics textbooks, they look at heat as some sort of substance and heat energy as something independent of kinetic energy. In our lessons, it is just one subset of kinetic energy.

Electrical energy
Electrical energy is the movement of electrons. That is kinetic energy. The voltage in an electrical circuit is the potential energy that can start electrons moving. Electrical forces cause the movement to occur.

Chemical energy
Chemical energy is potential energy until the chemical reaction puts atoms and molecules in motion. Heat energy (KE) is often the result of a chemical reaction.

Light energy
Light is the movement of waves and/or light particles (photons). It is usually formed when atoms gain so much kinetic energy from being heated that they give off radiation. This is often from electrons jumping orbits and emitting moving photons.

Nuclear energy
Certain elements have potential nuclear energy, such that there are internal forces pent up on their nucleus. When that potential energy is released, the result is kinetic energy in the form of rapidly moving particles, heat and radiation.

Summary
Energy is defined as the capacity to do work. An object has kinetic energy if it is moving. If there are some constrained or pent-up forces, preventing the object to move, the object is said to have potential energy. There are various subsets or forms of both kinetic and potential energy, such as heat, chemical, electrical, light and nuclear energy.



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  #3  
Old Saturday, October 04, 2008
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Kinetic Energy Concerns Movement of Matter


Kinetic energy is the energy of a moving object according to the equation KE = mv. This equation is valid provided that the speed of the object does not approach the speed of light. Motion and kinetic energy can be a direct result of a force can be applied to a object. Also, releasing potential energy can create kinetic energy, such as with springs and chemical reactions. Most forms of energy where material is moving are kinetic energy.

Questions you may have include:
  • What does the equation KE = mv mean?
  • How can a force create kinetic energy?
  • What are other forms of energy?


Kinetic energy equation
The energy of a moving object is called kinetic energy and is abbreviated as KE. The properties of kinetic energy are that the greater the mass of a moving object, the greater its energy will be. Also, the faster it goes, the greater its energy. That energy is proportional to the square of the velocity.

The equation for calculating the kinetic energy of an object is

KE = mv

where:

KE is the kinetic energy, usually measured in joules
m is the mass of the object, usually measured in kilograms
v is its speed or velocity of the object, measured in meters per second
v is the velocity squared or v times v
mv is one-half times m times v
A joule equals a newton-meter. Since a newton equals a kilogram-meter per second squared (kg-m/s), you can see that a joule equals kg-m/s. It is not usually designated that way, but you can see it holds by multiplying the units.

Example with different masses
If two objects were going at the same velocity, but one object had twice the mass of the other, then the energy of the heavier object would be 2 times the energy of the lighter object.

If M = 16 and m = 8

then KEM = *16*v = 8v

and KEm = *8*v = 4v

thus KEM = 2KEm

Example with different velocities
Now suppose the lighter object in the example above was going twice as fast as the heavier object. Say the object with m = 8 was going at v = 4 m/s and the object with M = 16 was going at V = 2 m/s. Then the energies would be:

KEmv = mv = * 8 * 4 * 4 = 128

KEMV = MV = * 16 * 2 * 2 = 64

Thus, the effect of higher velocity is greater than that of a greater mass.

Force results in kinetic energy
When a force is applied to an object, it accelerates the object according to the equation

F = ma

where:

F is the force, measured in newtons
m is the mass, usually measured in kilograms
a is the acceleration, usually measured in meters/second/second or m/s
ma is m times a

Acceleration is defined as the change in velocity over a period of time. Thus, if the force is applied to an object for a certain amount of time, it will reach the velocity v and have a kinetic energy of KE = mv.

Work
Work is defined as the result of a force applied over a distance, W = Fd. Since force is in newtons and distance is in meters, work is in newton-meters, which equals the units of energy, joules.

Other forms are also kinetic energy
Often, you will hear about other forms of energy, such as heat and electrical energy. In reality, they are also kinetic energy.

Heat energy
Heat is the movement of molecules. It is the sum of their kinetic energy. In many physics textbooks, they look at heat as some sort of substance and heat energy as something independent of kinetic energy. In our lessons, it is just another form of kinetic energy.

Electrical energy
Electrical energy is the movement of electrons. That is kinetic energy. The voltage in an electrical circuit is the potential energy that can start electrons moving. Electrical forces cause the movement to occur.

Chemical energy
A chemical reaction puts atoms and molecules in motion. Heat and radiation energy are often the result of a chemical reaction, which releases chemical potential energy.

Light energy
Light consists of the movement of waves and/or light particles (photons). It is usually formed when atoms gain so much kinetic energy from being heated that they give off radiation. This is often from electrons jumping orbits and emitting moving photons.

Summary
Kinetic energy is the energy of a moving object according to the equation KE = mv. Motion and kinetic energy can be a direct result of a force can be applied to a object. Releasing potential energy can create kinetic energy, such as with springs and chemical reactions. Heat, electrical energy and light are forms of kinetic energy.
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Potential Energy


Potential energy is when an object has the potential to create kinetic energy or related forms of energy. The object is in a state of equilibrium, where there is a force that is attempting to move matter and an equal other force preventing that movement. A good example of this equilibrium is the force that compresses a spring and the internal force trying to expand the spring. That internal force is considered the potential energy of the compressed spring. Common types of potential energy are elastic, gravitational, chemical, electrical and nuclear. When potential energy is released, it can be applied to do work.

Questions you may have include:
  • What is the state of equilibrium?
  • What are the types of potential energy?
  • How can potential energy be applied?


Equilibrium and potential energy
Potential energy is when two equal forces in opposite directions are applied to an object.

Force causes acceleration
When you apply a force to an object, it will accelerate while that force is being applied, according to Newton's Second Law and the equation F = ma, where:

F is the applied force in newtons
m is the mass in kilograms
a is the resulting acceleration in meters/second-squared
1 newton = 1 kg-m/s.

Resistive force can result in potential energy
But this simple equation or relationship goes under the assumption that there are no other forces resisting that motion. If there is some force such as friction that resists the motion, the acceleration would be a = (F - Fr)/m, where Fr is the resistive force.

Now if Fr is equal to the applied force F, the acceleration and movement would be zero. But if the force F is still being applied, then there is potential energy that would be released as soon as Fr is taken away or reduced.

Example
For example, if you are in a car on a hill, the force of gravity Fg is trying to roll the car down the hill. But if you have the brakes on, the resistive force Fr is holding you back. Fg is the potential energy. Now if you slowly release the brakes, that potential energy will change to kinetic energy as you start to roll down the hill. Applying the brakes again will bring you back to a state of potential energy, as long as you are on the hill.

Types of potential energy
There are situations when an object has the potential to start moving and gain kinetic energy. Often there are forces acting on the object, but the forces aren't yet sufficient to move the object. Common types of potential energy are:

Elastic
Gravitational
Chemical
Electrical
Nuclear
Elastic potential energy

When you compress a spring, you create potential energy. The force of compression is proportional to the compression, according to Hooke's Law. Releasing the spring turns the potential energy into kinetic energy. the spring can be then used to propel some object.

A balloon is another example of elastic potential energy, where the air is compressed within the balloon. Breaking the balloon with a needle will turn the potential energy into kinetic energy of rapidly moving air molecules.

Gravitational potential energy
An object held above the ground has a potential energy related to the height at which it is held, according to the equation

PE = mgh

where:

PE is the potential energy
m is the mass of the object
g is the acceleration of gravity constant (32 ft/s or 9.8 m/s)
h is the height above the ground or the distance that the object falls
mgh is m times g times h
If you drop the object, its potential energy will become the kinetic energy of motion (PE = KE). Since PE = mgh and KE = mv, then mgh = mv.

You can determine the speed it will be traveling after falling a height h by solving the equation for v:

v = 2gh

v = SQRT(2gh) = √(2gh)

SQRT(2gh) and √(2gh) means the square root of 2gh. Note that the mass m cancels out of the equation, meaning that all objects fall at the same rate.

Thus, if h = 1 ft, and since g = 32 ft/s, then v = 2 * 32 * 1 = 64 and v = 8 ft/s.

Chemical potential energy
Some unstable molecules such as nitroglycerine have potential energy ready to be released under the right conditions. The release may be an explosion, giving off kinetic energy in the form of light, heat, and moving particles.

Certain mixtures of chemicals can reactalthough not so violentlyto create heat and other forms of kinetic energy.

Electrical potential energy
An electrical outlet in your house has the potential energy of 110V or 220V, depending on the country in which you live. Once an electrical circuit is established, that potential energy becomes the kinetic energy of the movement of electrons, as well as heat and other effects.

Nuclear potential energy
Some atoms have an unstable nucleus that has the potential of splitting and releasing kinetic energy. For example, Uranium-235 is unstable and can split in two, releasing high speed subatomic particles and radiation. Its potential energy is turned into kinetic energy.

Applications of potential energy
Controlling the release of potential energy can result in it performing useful work. We use springs to help close doors in our houses. Dams and electrical generators use the potential energy of water to create electrical power. We burn fuel to propel our automobiles and heat our homes. We release the potential energy of electricity to operate our appliances. Nuclear potential energy is also used to create electricity.

Summary
Potential energy is when an object has the potential to create kinetic energy or related forms of energy. The object is in a state of equilibrium, where there is a force that is attempting to move matter and an equal other force preventing that movement. Common types of potential energy are elastic, gravitational, chemical, electrical and nuclear. When potential energy is released, it can be applied to do work.
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Simple Machines


A machine is a device that helps people do work against some resistive force. Some machines are powered by engines, motors and even animals, while many others simply use human power. The basis of all complex machines comes from their simple components. When these components are by themselves, they are called simple machines. The most common simple machines are the lever, rollers, the ramp, and the pulley.

Questions you may have are:
  • What is the background of machines?
  • How does a lever, roller, and pulley work?
  • What about machines that run forever?


Background of inventions
Before engines and motors were invented, people had to do things like lifting heavy loads by hand. Using an animal could help, but what they really needed is some clever ways to either make work easier or faster. Ancient people invented, simple machines that would help them overcome resistive forces and allow them to do the desired work against those forces.

Ancient Egyptians
The ancient Egyptians, for example, used such inventions to help them build the pyramids. They used levers to pick up large blocks of stone. They put those blocks on rollers to move from one area to another. Then they used ramps to move the blocks up to the top of the pyramid they were building.

Ancient Romans
The ancient Romans used catapults to throw stones at their enemies. The catapult was a large lever. They used a pulley to pull down the arm of the catapult. The device was set on wheels--an advanced version of rollers--to move it from place to place.

Today
We still use those simple machines today, by themselves and as part of more complex machines.

The lever
In order to lift up a heavy object, such as a huge rock, the lever was invented. We still use it today to lift things. It also can be used as a teeter-totter and a catapult.



Suppose you wanted to lift up a box that weighed 200 pounds. If you used a lever with the distance from the pivot point or fulcrum F to the weight RA = 1 foot and the other distance EA = 10 feet, then you would only have to push down at E with 20 pounds of force.

This is because of the rule that E * EA = R * RA. In other words,
20 pounds times 10 feet = 200 pounds times 1 foot.

Although you have what they call a mechanical advantage in being able to lift this heavy weight, you are actually doing the same amount of work, because you have to push the 20 pound force 10 times as far as the 200 pound box moves. For example, to life the box 3 inches, you have to push the 20 pound force for 30 inches.

Since Work is Force times Distance, then you can see that:
20 pounds x 30 inches = 200 pounds x 3 inches.

(NOTE: I am using English units of measurement here. All of this holds true for metric units as well.)

Teeter-totter
A teeter-totter is a lever that children use as a play thing. Since the children are usually approximately the same weight, the fulcrum is placed in the center of the board.

A child sits on each end of the board, and they take turns lifting each other off the ground.

Catapult
A catapult is a lever in reverse. A heavy weight is dropped on the short side of the level, catapulting a lighter weight from the longer side of the lever. This works because not only does the weight on the long arm of the lever (EA in the picture above) travel a greater distance, but it also goes faster.

If EA = 10 feet, RA = 1 foot, and you drop R = 200 pounds at 32 feet per second, weight E = 20 pounds will fly in the air at 320 feet per second!

Different configurations
There are different configurations for levers, where the fulcrum is placed on one end or the other. The principles still hold.

Rollers
The resistive force of friction is one of the first thing ancient people wanted to overcome. In order to construct buildings they had to drag large blocks from one place to another. Friction made the job difficult.

One way to reduce friction is to lubricate the sliding surface with oil. But this was not practical in most situations. Then someone came up with the idea of placing logs or rollers under the object, so that the friction was greatly reduced.



They used a lever to lift the object onto the rollers, and then used the rollers to reduce friction and easily move the heavy object from one place to another.

After hundreds of years, rollers were replaced by the invention of the wheel on an axle. A wheel is simply a refinement of the roller.

Movers use a rack with wheels called a dolly to move heavy furniture. Where else have you seen wheels being used to reduce the force of friction?

Ramp
Although rollers reduce friction, a ramp may be used to gain a mechanical advantage or to reduce the amount of force required. But remember that the amount of work required is the same (not counting the losses due to friction).

A ramp is also called an inclined plane. By rolling an object up a hill or a ramp, you require less strength than required to pick the object up the same height, but you compensate by traveling a greater distance. This ability to move an object to another height works the same as with a lever.



If you lifted a barrel that weighed 200 Newtons up 6 meters in height, the work against gravity would be 200 x 6 = 1200 Nm. If you rolled that barrel up a ramp 12 meters long, you would only have to push with a force of 100 N. That is because 200 x 6 = 100 x 12.

(Note that by rolling instead of sliding, you are drastically reducing the extra resistance from friction.)

Variations on the ramp or inclined plane include the door-jam or wedge and the threads of a screw or bolt. Threads are simply a ramp that are wrapped around a cylinder like a bolt.

The pulley
A pulley is a way to use your own weight to lift an object to another height. The same force must be used, but it simply changes direction. You pull down and the weight goes up.



Perpetual motion machines
Many people have tried to invent a machine that would run forever, once you got it started. They call such a machine a perpetual motion machine.

Of course, the big problem with a machine running forever concerns the losses due to friction. To overcome those losses, many of these machines have been designed to use gravity for power. Unfortunately, that just doesn't work. Like the saying goes, "What goes up must come down."

There are other machines that improve their efficiency by using other means of power. An inventor recently came up with an automobile with a large flywheel. When the car went downhill, the flywheel would gather energy to be used when the car went uphill. But it still needed an engine to make up the difference of what was lost due to the resistive forces.

In conclusion
Simple machines usually exchange using a smaller force over a greater distance to move a heavy object over a short distance. The work required is the same, but the force required is less. The are also simple machines that help to reduce the resistance of friction or such.




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