Ch+5+-+Work+and+Energy

=__ Chapter 5: Work and Energy __=

http://www.rlasd.k12.pa.us/teachers/bsmith/honors/hpch05/hpch5.html Above is a link to the Chapter Five page, where you can find notes, practice problems, and assignments.

Important Concepts in this chapter:

 * Work
 * Work-Energy Theorem
 * Conservative vs. Non-Conservative Forces
 * Potential Energy
 * Gravitational potential energy
 * Elastic potential energy
 * Kinetic Energy
 * Conservation of Mechanical Energy
 * Power

= = = __Work__ = = media type="file" key="Wikispace.mov" width="300" height="300" = This video demonstrates work. Work - applying a force **through a distance** Work is a scalar quantity. The force and distance are in the same direction.

**No Work** :

media type="file" key="workvideonowork.mov" width="300" height="300"



**W = F∆x**
Work is measured in Joules (J). J = N*m

On a Hill: **W = Fcosø (change in x)**

**Net Work:** - sum of the total work (scalar addition) -can include KE, PEg, and PEe

** Negative Work: ** - force acts opposite to direction of motion

On a Force vs. Distance Graph, the work is the area under the curve

//Sample problem:// //An 80 kg person carries a 25N package up a flight of stairs. The vertical height of the stairs is 10m.// //F = mg// //80kg(9.8)// //784 N + 25N package// //809N// //W = Fd// //W// //809N(10m)// //8.09 x 10^3 J//

= __Work-Energy Theorem__ =

The work-energy theorem states: When work is done by a net force, on an object, and the only change in the object is its speed, the work done is equal to the change in the object's kinetic energy.

Energy is the ability to do work and work is the ability to apply some force through some distance.  Types of Energy:
 * Kinetic - energy of Motion (1/2mv^2)
 * Potential - energy of Position (mgy)

This picture is similar to what we tested in our Work = Energy lab.

= __Conservative vs. Non-Conservative Forces__ =

//Image source: http://en.wikipedia.org/wiki/Conservative_force// Look at the picture to the above. This is an example of conservative forces. The path the object takes does not affect the energy that it possesses at both instances.

Non Conservative Forces A force is non-conservative if the work it does on an object depends on the path taken - friction - takes longer to push = more work A force is conservative if the work does not depend on the path. An example of this would be gravity. The path is always the same. You are not a conservative force, because the amount of work performed depends on the path taken.

If a box on a floor is being pushed along a straight path, less work is done than if it is pushed along a curved path. This is because of the work of friction, which is a non-conservative force.

=__Potential Energy__= Potential Energy is the stored energy. Potential Energy Types Gravitational - ability for gravity to pull an object through some distance Elastic(Springs) - ability for a spring to push or pull an object through some distance  Gravitational Potential Energy (GPE) PE = mgy change in PE - units are joules

= __Kinetic Energy__ =

= = // 1/2 m(v^2) // // 1/2mv^2 - 1/2mVo^2 // KEf - KEi = change in KE(Kinetic Energy) When work is done by a net force on an object and the only change in the object is its speed, then the work done is equal to the change in the object's kinetic energy. = This picture shows how the ball at the top only has potential energy, and then when the ball is released it gains kinetic energy, or the energy of motion. media type="custom" key="3121758"

http://videos.howstuffworks.com/hsw/6175-work-and-energy-energy-video.htm This is a link to a great video of examples of potential and kinetic energy, such as roller blades and roller coasters. This video is about Potential and Kinetic energy and how they are the same.

media type="file" key="animoto_video.mp4" width="300" height="300"

//Image source: http://en.wikipedia.org/wiki/Kinetic_energy// On a roller coaster, kinetic energy is the greatest at the bottom of a hill because it is moving the fastest. As it goes up the next hill, it loses kinetic energy and gains gravitational potential energy.

//In this equation, the term x-xo is replaced by s which represents the displacement total distance. v2 = v02 + 2as therefore, a = (v2 - v02 ) / 2s Applying the Newton’s Second Law of motion, since F=ma, you get F = ma = m (v2 - v02) / 2s and multiply the distance s for work then break it and you get: W = Fs = 0.5mv2 - 0.5mv02 The kinetic energy (KE) is defined as: K = 0.5mv2 It must be noted that this quantity will be a non-zero scalar quantity. -source kinetic energy// = =

= =

=//__Conservation of Mechanical Energy__//= //symbol: E (the sum of)// //Total energy an object possesses (adding all of the energies together)// //Kinetic energy = (1/2mv^2)// //Gravitational Potential energy = (mgy)// //Elastic Potential energy = (1/2kx^2)//  //Conservation of Energy without friction// //the total mechanical energy remains constant// //E(initial) = E(final)// //KEi + PEi = KEf + PEf//

//An example problem of this would be if an object was dropped at rest from 55 cm above. An unstretched spring compresses the spring 15 cm. The object has a mass of 2.6 kg. Determine the spring constant.// //E1 = E2// //PEg1 + PEs1 + KE1 = PEg2 +P// //Es2 + KE2// //mgy1 = 1/2kx2^2// //(2.6)(9.8)(.7m) = (1/2)k(.15^2)// //**k = 1,585**//

Non Conservative Forces (with friction) another way to write conservation of energy is change in KE + change in PE = 0 Wnc = Fd Ei - Wnc = Ef Wnc = (KEf + PEf) - (KEi + PEi) (KEi + PEi) - Wnc = (KEf + PEf) media type="file" key="spring.m4v" width="300" height="300" This video demonstrates Elastic Potential Energy because when the ball is compressed in the launcher it has only Elastic Potential Energy.

An example of a problem using non-conservative forces would be a spring acting on a ball. The first thing needed to know about a problem involving a spring would be the formula for energy of a spring. So the potential energy of the spring is added to the initial position side of the equation to look something like PEi + PEspring + KEi equals PEf + KEf. In this particular problem, if the PE is 0 is at the bottom where the ball starts, everything except PEspring and PEf cancel out. So PEspring = PEf. Now it becomes a simple plug and chug equation. And who doesn't LOVE those? **This same basic concept can be applied to any non-conservative force, but something like friction will have to be subtracted instead of added.**

Conservation of Energy - General Energy cannot be created or destroyed. It can be transformed from one form to another, but total amount remains constant (chemical, magnetic, kinetic, nuclear)

Ways to Transfer Energy: Work - apply a force through a distance Heat - microscopic collisions Mechanical Waves - sound, water waves Electrical Transmission - circuits Electromagnetic Radiation - light, radio, microwaves
 * We may learn the rest later, but we don't need them now!***

= __Power__ = Power power is the rate at which work is done P = W/t = joules/sec

Power Units

= = MKS- J/s = W(Watt)

= J/s = W(Watt) English = ft/lb 550 ft lb/s = 1hp(horsepower) 1 hp = 746 W

[[image:http://farm4.static.flickr.com/3148/3028364267_91fd96d897.jpg width="330" height="253"]]
Photo: A 800 (gasp!) horsepower engine James Watt invented the unit of horsepower and it is equivalent to the work that "the average horse can do". (It is, however, not always seen as a very correct/appropriate way to represent it)

P

= F(x)/t = F(v) P- W/t = m*a*d/t

t = p/w kWh- unit of energy (bill for work energy)

Movement is not the only thing that does work. Let's say the light bulb below is a 100Watt light bulb. so 100W = W/t.

= = ([|photo credit])

Say for instance that the light is on for five seconds. 100W = W/5, so this light bulb performs 500J of work.

=__Miscellaneous__=

__Force vs. Distance Curve__ The area under the curve is work

__Center of Mass(CM)__ A person has a mass which is spread throughout the body and CM is the point at which all mass is considered to be concentrated. (Center of mass does not only apply to humans. Any object can have a center of mass)