1) What is Energy?

This fun video sings about the basic facts of energy:

Energy is the ability to do work and cause change. Energy exists in several forms such as heat, kinetic, or mechanical energy, light, energy, electrical, or other forms. http://physics.about.com/od/glossary/g/energy.htm Energy can never be created nor destroyed (check #10 below for more information); however, it can change into different forms listed above.
Energy is a property; therefore, it is intangible. Thus, no object can be "made" of energy.

Types of Energy

1. Gravitational potential
- Steps to get to equation: W=fd àW=ΔEp àEp=ΔEgàΔEg=mgh (weight*height)
- Gravitational depends a lot on the Distance
- It also depends a lot on the Force
2. Chemical potential
-ex: chemical energy stored in food to give our body the ability to go to school and study or chemical enery in gasoline to power our cars
3. Thermal (heat)
- Thermal energy is heat energy. It is the state of energy that all energy returns to and is essentially "useless".
4. Elastic potential
- A.k.a spring energy
equation:Es= ½ kx²
5. Mechanical
- Mechanical energy describes the sum of the kinetic and potential energy in a mechanical system.
6. Kinetic
Energy of motion
- Depends on two variables:
1. mass
2. velocity
equation: Ek= ½ mv²
7. Nuclear
- Nuclear energy is released by the fission (splitting) or fusion (merging) of the nuclei of atoms.
8. Solar/Radiant
- Solar/Radiant energy is derived from the sun. It takes the form of sunlight and heat from the sun.
9. Electromagnetic
- Electromagnetic energy is energy in the form of electrical charges, magnetic fields, and photons

This video gives a visual explanation to Elastic Potential Energy being converted to Kinetic. This video is taken from a roadrunner episode and the different aspects of physics are pointed out in it. Elastic to Kinetic is displayed through a spring which then snaps and sends someone flying... It is also displayed through the compression in a spring which yet again sends someone flying into the air....

2) What is Work?

Work is the transfer of energy. Work is done on objects to give them energy, or the ability to do work. Work is NOT a form of energy, but a way of transferring energy from one place to another or one form to another. Therefore, work and energy are very closely related. Like energy, work is measured in Joules (J).

work=force*distance (W=fd)

external image lifting_weights_op_446x600.jpg

Work is dependent upon distance; therefore, you only do work on something if you move it. For example, when you lift weights, you're doing work on the weight because you've shifted its position.
external image The_man_pushing_the_wall_by_27Kingdom.png

You can push onto a wall all day and think you've done tons of work; however, 0 Joules of work was done because the wall was not moved from its original position.

3) Spring Lab

In class we did an experiment with springs to determine the relationship of the force and spring stretch length. We attached a spring to the clamp and added on kilograms to stretch out the spring. We then measured the spring's length after each amount of mass we put on. We started with 0.2 kilograms and kept adding on more until we got up to 1.2 kilograms. Then we took off the mass and measured the spring again each time we took off .1 kilograms. After collecting the data, we put the information into Logger Pro and it created a graph for us. Since both of the graphs were lines, we know that the relationship between the force and the stretch length is linear because the intervals between each point were constant, and therefore, we use the equation y=mx+b. The slope of the graphs represented the spring constant (represented by the variable k and measured in N/m), which is the stiffness of the spring. This equation then became Force=spring constant*stretch length, or F=kx. We also learned about work through this experiment. While learning about work, we also came up with a second purpose: how much work was done on our spring? We derived the answer using the equation, A=1/2bh, which is used to find the area of a triangle and applied to the area under the graph which is also called the integral. This equation became work=1/2(spring constant)(stretch length)2, which can also be stated as W=1/2kx2. We learned that springs stretch and unstretch in the same way.


These two graphs display the relationship between Force and stretch Length or F=kx. As explained above, the relationship is a linear equation with Force (F) and Stretch Length (x) being the variables, and Spring Constant (k) being the constant slope. As explained above as well, the integral (area underneath the graphs) represents the word done on our spring. We derived the equation, W=1/2kx^2, through these two graphs.

The negative sign in Hooke's Law: F=-kx:
The negative sign in Hooke's Law: F=-kx does not mean that the spring constant is negative. It rather means that the force acting on the spring (the tension force) is in the opposite direction as the stretch length of the spring (x).

4) Rubber Band Lab

In class, we did an experiment similar to the spring lab, but instead of using springs, we used rubber bands. Our purpose was to find out if rubber bands also obey Hooke's Law. Instead of using a spring, we hung a rubber band and added weights in increments of 0.1 kilograms until the rubber band held a total of 1.05 kilograms, to stretch out the rubber band. As the rubber band stretched, we used a meter stick to measure it (in meters). Then, we took off weights in increments of 0.1 kilograms and measured the length of the rubber band. With the data, we created two tables, one representing the "stretching" data and the other, the "unstretching" data. After collecting the data, we put the collected information into Logger Pro, where it calculated both the Force and stretch length. Using this data, we created 3 graphs, one representing stretching Force vs. stretch length, one representing unstretching Force vs. stretch length, and the last one with both graphs incorporated into one. The graphs were non linear, meaning rubber bands do not follow Hooke's Law, and therefore, rubber bands and springs do not stretch in the same way. Rubber bands are inelastic because they do not follow Hooke's Law.
The graphs showed us that the rubber bands created a hysterisis loop, a system in which the energy input is greater than the energy output, meaning energy was lost in the process of stretching the rubber band.
These graphs display the results of the Spring Lab. If compared to the graphs of the spring lab, it is apparent that the two are not very similar; whereas the spring lab displayed to lines describing Hooke's Law, these graphs display that the rubber bands created a hysterisis loop. In this system the energy that is put in is greater than the energy that comes out of it. Therefore rubber bands do not follow Hooke's Law.
5) F=-(kx): Hooke's Law
​Hooke's Law, derived by Robert Hooke, describes the relationship between Force from the spring applied to the weight and the stretch length of the spring. According to Hooke's Law, the relationship is linear and can be represented by the equation, F=-kx, where F is force (N), k is the spring constant (N/m), and x is the stretch length (m). Springs stretch and unstretch in the same way. An object that follows Hooke's Law is elastic. When graphed, the graph of an elastic object should be linear.

Picture of Hooke's Law

This video is one made by a physics student that shows something similar to what we did in our "Spring Lab". A spring is attached to a rod and then ten 100 gram masses are added to the spring one by one. They then record the length of the spring and figure out the stretch length. This video helps give an explanation to Hooke's Law in a visual way. It is also another reference to our "Spring Lab".

6) Power

Power is how fast work (rate at which work is done) is done or how fast energy is transferred.
P=w/t à ΔE/t
Power is measured in watts (W; equal to Joules over seconds) or horsepower.

7) E=mc^2

Whether or not one has sat in a physics class or not, they have most likely heard of this equation that Albert Einstein derived. If read out loud, it would read "Energy is equal to mass multiplied by the speed of light squared." But what does this really mean? Through this equation Einstein explained that mass and energy are equivalent to one another. This equation exhibits how much energy is stored in a given mass, or vice ver​sa. Very small amounts of energy may be converted to mass or likewise. Also, when one adds energy to something such as a spring, mass is gained as well. This [[@http://www.btinternet.com/~j.doyle/SR/Emc2/Basics.htm#What Does the Equation Mean?%7C|E=mc^2 website]] not only explains the equation, E=mc^2, in further detail, but also gives explanation to what each letter stands for in the equation, a simple experiment that models how fast the speed of light really is, and Einstein's explanation himself for E=mc^2.

8) Net Positive Energy

What does the phrase "Net Positive Energy" mean?
To produce energy or gain access to energy sources, such as oil, people have to put in energy. To get a net positive energy, you have to put LESS energy into the process of getting the energy than the actual amount of energy you get out. There are houses called net positive energy homes that actually make more energy than they use so the energy companies pay the owners. Check out this website to learn about net positive energy homes:
http://www.energybuilder.com/what-we-do.htm. Hybrid cars are cars that run partly on energy and when the energy runs out they run on fuel. You spend more money up front on hybrid cars, but you break even in about five years because you don't have to spend as much on gasoline. However, cars in general usually need the battery replaced every few years so hybrid cars probably don't have a future.

9) Potential Curves and Potential Energy

Potential energy depends on distance and force. The "zero point" of potential energy is when the force is virtually zero. On a potential curve, the force is always the opposite sign of the slope. A potential curve is much like a roller coaster. The first drop is always the largest and the car always returns to it's original height. An equilibrium point is stable if the system always returns to it after small disturbances. If the system moves away from the point, it is unstable. This game lets you experiment with building roller coasters, which are potential curves. The game is actually very realistic because the car can fly off of the track if you don't structure is right! Try it here.

10) Law of Conservation of Energy
There are different types of "conservations." There is conservation of momentum, angular momentum, and energy. The conservation of energy states that no amount of energy is changed; it is neither lost nor gained in a closed system. Energy can, however, change into different forms.

Examples of Conservation of Energy:
-This website attached is a story about "Denis the Menace" concerning "Law of Conservation of Energy." http://web.cc.uoa.gr/~pji/Feynman_Lectures_on_Physics_Volume_1_Chapter_04.pdf
-Another example of law of conservation of energy is a person dropping a tennis ball from the top of a building. The ball does not lose energy, but rather transfers the gravitational potential energy into kinetic energy. The ball begins with gravitational energy (Eg=mgh) and the energy transfers into kinetic energy (Ek=1/2mv2). In order to solve problems using the "Law of Conservation of Energy," one must use the eqation Egi+Eki+Esi= EgF+EkF+EsF, and cross out the types of energy that do not apply, then plug the equations in for each type of energy that is involved in the problem, and solve.

If the amount of energy always stays the same, why are people so worried about conserving energy? It is true that the total amount of energy never changes; however, the amount of different kinds of energy (chemical, electric, mechanical, etc.) changes constantly. When people "conserve" energy, they're trying to prevent all the energy from going "useless"---in other words, preventing all the useful energy (like chemical energy in fuel to power our cars, for example) from turning into heat energy. Heat energy is a useless form of energy; we can't use it to power anything.

11) Projectile Motion of a Spring

1. Position vs. Time, Velocity vs. Time, Acceleration vs. Time
On the first graph (position vs. time), it shows the stretch length of the spring at 0.5 seconds is .64 m. The weight at this moment is at the bottom of its bounce, stretching to its maximum stretch length. This graph is a “sine” graph, meaning it represents the bouncing weight at any particular time, making the graph curvy. The second graph (velocity vs. time) shows the velocity of the weight at 0.5 seconds is 0 m/s because when the mass is at the bottom of its flight, it momentarily is not moving. Again, this graph is a “sine” graph, because the velocity of the weight is increasing and decreasing as the spring stretches and unstretches. The third graph (acceleration vs. time) shows the acceleration of the mass at 0.5 seconds is positive 1.2 m/s2 because it is at bottom of its flight, which means the tension force is about to win, causing the spring to go down, and making the acceleration positive. The graph takes this shape because the forces applied on the weight switches from the tension force winning to gravity winning, and it continues this pattern as the spring bounces up and down.
2. Force vs. Acceleration
In the Force vs. Acceleration graph, we observed this relationship between force and acceleration was linear. This graph follows Newton’s 2nd Law: F= ma because the mass multiplied by acceleration equals a force. Our slope is equivalent to our mass because the units used for slope N/m/s/s is equal to a kg, which is also the unit used for mass. The slope of our line is 1.066 N/m/s2, and this is correct because it should be ideally a little over 1 N/m/s/s because the mass we used was one kilogram, and we also had some small outside mass from the equiment we used in our experiment.
Force vs. Stretch length
On this graph Force is plotted on the y axis and stretch length is plotted on the x axis. The relationship of Force and stretch length is linear with a negative slope. This graph follows Hooke’s Law: F=-kx. The slope represents the spring constant (-24.67) but ideally this should be 25 because this is the stiffness of our spring, or the spring constant, so it cannot be negative. However, the negative sign is not applied to the value for "k" but to the stretch length. The negative sign means that the stretch length and tension force are in opposite directions.
Spring Energy, Kinetic Energy, Total Energy vs. Time
On the Y axis of this graph, all three energies used in the lab are plotted: spring energy, kinetic energy, and total energy. On the X axis, is the time. The trend of the total energy is constant because throughout the experiment the total energy is conserved. The spring and kinetic energies are equal and opposites throughout the bouncing because when one force is at its maximum the other force is at its minimum. But when the spring is at its equilibrium, in the middle, the two forces are equal. If the graph appears slightly curvy this is due to experimental error, or occasional energy being transferred into heat energy, but for the most part, energy is conserved.

http://www.walter-fendt.de/ph14e/springpendulum.htm (This website enables you to change the spring constant, mass, gravitational acceleration, and amplitude of the spring and see how it affects how it bounces. You can also view what velocity, acceleration, force, and energy are doing during the bounce, and at what points are their maximum and minimum.)
*From Mrs. Wyatt's Delicious.com*

12) Pendulums
pendulum picture
pendulum picture

For a pendulum, the amount of time it takes for a bob, the object attached to the end of a spring, to make its cycle is called a "period." Wondering what affects how long it takes a bob to make its cycle, we did an experiment envolving a pendulum, bob, and spring. We wanted to test whether mass, length of string, or height of release (amplitude) had an affect on the period of a pendulum. We timed the periods for different amounts of mass, lengths of string, and sizes of amplitude while keeping two of our variables controlled. As we entered our results into LoggerPro, our graphs showed us only the string length had an affect on the the period of a pendulum. We also concluded that gravity had an affect on the period of a pendulum.
http://www.lon-capa.org/~mmp/kap13/cd363a.htm *This applet allows you to play around and conclude yourself how gravity and string length has an affect on the period of pendulum. (Thanks to Mrs. Wyatt's Delicious.com website)*

Physics for Future Presidents

ENERGY: Ch. 5 Key Energy Surprises

Why We Love Oil
  • Oil carries huge amounts of energy (that's why we love gasoline)
  • Gasoline must combine with oxygen to provide its energy
    • When gasoline burns or explodes, the hydrogen combines with oxygen to make water and carbon combines with oxygen to make carbon dioxide.
    • oxidizer: type of chemical which a fuel requires to burn. E.g: gunpowder uses potassium nitrate in place of oxygen as its oxidizer
  • Gasoline carries more energy per lb than food.
    • people eat on average 1-2 lb of food a day
    • enormous amount of energy in food is also what makes it so difficult to lose weight.
  • Alternatives to gasoline:
    • gasohol: ethanol mixed with gasoline. Makes little difference in reducing pollution
    • butanol possible biofuel of the future because of its high energy density. Gasoline only 1.1 times the energy of butanol.
  • Hydrogen gas or liquid is 2.6 times better than gasoline (energy/lb)
    • but a pound of hydrogen takes up a lot more space, so it actually has 4.5 times less energy per gallon
    • Can't mine the gas from Earth; to use hydrogen it must separate from other atoms - by electrolysis (running electric current through hydrogen)
    • 1 way to get net positive energy from hydrogen: obtain it from natural gas.
  • Antimatter & hydrogen gas: neither one is a source of energy, rather, both are means of transporting energy

  • Power is the rate energy is used. Measured in calories/hr or joules/sec.
    • Gasoline has more energy than TNT, but TNT can deliver more power than gasoline because of the faster speed of deliverance.
  • Same amount of energy can be delivered at different rates or different powers
  • 1 horsepower = 1 kilowatt
  • Solar power = 1 kilowatt/sq. m
  • Watts are used to measure electric power.
  • Kilowatt-hour (kWh): amount of energy if you used a kilowatt for 1 hour. Total amount of energy delivered.
  • Kilowatt is the rate of energy delivery (power)
    • 1000 kilowatts = 1 megawatt (or 1 million watts)
    • 1 billion watts = 1 gigawatt
  • 1 kWh = 1000 food calories
  • Below is a video that explains how solar panels work, and how the energy from the sun is converted into electricity by the solar panels.

Energy Alternatives
  • Fuel is used in four different ways: transportation, electricity, heat, industry
  • Diversity of sources more important fact; we must address several sectors to reduce fossil fuel emissions

The Bottom Line: The Cost of Energy
  • For the same energy, coal in the US is 20 times cheaper than gasoline. 0.4-0.8 cents/kWh ($40-80/ton)
    • developing nations are likely to rely on coal for their energy needs
  • The price we pay for fuel depends on energy that it delivers and convenience
  • Challenge for alternative energy sources is to be more economically viable than coal

The Physics Of Ballet

Why Gravity Causes Things to Fall
Ballistic Calculator