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Wednesday, 7 December 2011

What is Energy?

Renewable Energy, Wasting Energy, 'He's Got Too Much Energy' - None Of These Are True. So What Is Energy?

We have all heard of energy. A word used in all sorts of situation. Energy in food, people and objects are all very common things to hear, but what exactly is energy? Well the easiest way to describe energy is through the statement: Energy is the ability to do work. Ok...That doesn't bring us any closer to knowing what energy actually is, so let me first start of by explaining Work:

Before we all get confused, physical Work is not work in the sense that we use it everyday. The incredibly clever person in your class, who does extra homework does not have more energy than you. Work, shown with the letter W, can be expressed easily with this simple formula:
W = Fx
In words, this means that the work done is the Force applied to an object multiplied by distance.  For example, if I am pushing an object with a force of 10 Newtons, and I push it 5 meters, the work done would be 50 Joules, 10 x 5, because F (the force) is 10 and x (the distance) is 5. 
As you can tell Work is very simple. The only thing you need to remember when thinking about Work is that the distance is not just any distance, it is the distance in the direction of the force. This may not seem very significant, but let me give you this example: If I have a steel ball suspended by a string. I start spinning it around, in a circle of circumference 5 meters, with the same force as before, 10 newtons, and it does one rotation. Surely the work done would be the same as in the first example?

 
Firstly, when looking at the work done, you have to analyse the forces. As we can see, the only two forces acting on the ball is that of me, which is F1 and that of the string, F2. The string is pulling the ball towards me, whilst, to keep the ball spinning, my force is at a right angle to F2. The resultant force is in a different direction than either F1 or F2, therefore, there is no work done.

So now that we know what work is, we can move on to energy. If I asked you to list all types of energy you knew, what would you say? If you said Nuclear, chemical, electric, thermal etc. you would be right, but they can be put more simply into two groups, potential energy, Ep, and kinetic energy, Ek. An object has kinetic energy when it is doing work, this can be in the case of electrical energy, in an exothermic reaction or simply when something is moving. An object has potential energy when it has the capacity to do work due to it's position or configuration. This can be in the case of a compressed spring, something being held any distance above the ground or, in fact, any matter, as famously described in Einstein's E=mc2, anything with mass also has energy.

Both of these types of energy have formulas to work out their values. These will change for certain situations, for example, with electrical energy, but in simple mechanics the formula for kinetic energy is Ek=12mv2 and the one for gravitational (potential energy possessed by an object due to it being pulled by gravity) potential energy, in it's simplest kind, is Ep=mgh. Both of these equations can be obtained using the equation for work, as previously mentioned, and Newton's second law: F=ma.
The potential energy equation is very simple. If you substitute ma, from F=ma, into the definition for work , Fx , for the F, you get: Ep=max. When using this to describe gravitational potential energy, you can substitute h, the height the object is lifted too, in for x, which just means distance. As we know, gravity is just an acceleration. The earth's gravitationally constant is 9.81m/s2 so we can put g in for a. That is how we get to the equation Ep=mgh.
The kinetic energy equation is also very simple. One of the main equations of motion is that final velocity squared equals initial velocity squared plus 2 times the acceleration times the time taken, or v2=u2 + 2ax. I do not feel it is relevant to explain how we got this equation, although, if the idea is popular, I may do a post on the basics of mechanics. Mainly Newton's laws of motion and the equations of motion, but anyway, kinetic energy: In a system with kinetic energy, the object must have started at a stop. Therefore the initial velocity is 0 and can be removed from the equation. Now we have v2=2ax. The equation F=ma can also be expressed as a = Fm and therefore we can change our equation to v2=2Fxm. Look what we have found! Above the m is Fx, or work done, and energy is the just the ability to do or be doing work, so, by rearranging the equation we get: Ek=12mv2.
So now we understand energy, right? Well first there are a few things to go over. Energy does not get destroyed or created. When I drop a pen, no energy is being lost, or created. Instead the potential energy of the pen is being converted into kinetic energy. In fact, if we forget about friction, all of the potential energy is lost over the fall. Let me give you an example: I lift a pen, mass 1kg (It is a heavy pen) 3 meters and then drop it. What is the velocity when it hits the ground?
 
Since we are ignoring friction, we know that:
   Loss in Ep= Gain in Ek
    mgh =12mv2
1Kg x 10m/s2 (We are rounding this up, gravity is actually more like 9.81 m/s2) x 10m= mgh
         12mv2 = 12 x 1 x v2  
0.5v2 (Kinetic Energy) = 30J (Potential Energy)
   v2= 60J
     v ≈ 7.45 m/s

The amount of energy in a isolated system, even in the air or other apparently inactive objects, must be the same, no matter what form they are in. This is the law of conservation of energy!

Now we understand energy. It isn't a physical particle or even a force, but instead a capability to do something. For the next section, let me ask you a question. If you take a large piece of coal and burn it, and then take a spatula of gunpowder and light it. Which reaction would you say is more violent? Probably the gunpowder, but the coal released more heat, and therefore, we will assume, it had more energy. Why does this happen? Well it is all down to something called Power:
Power is the rate at which work is done. It is given by the formula: P=Wt . P is power, W is work done and t is time taken to do the work. Therefore, even though the coal does more work, the gunpowder does it's work in a shorter time and is therefore more powerful.

So those are the basics of energy. Of course, there is further you can go, looking into the different forms of potential energy, for example. In fact, string theory, something I looked at in my last post, says that ever bit of matter, when broken down as far as you can, past atoms, protons, electrons and quarks are just 1 dimensional strings of energy. So next time you hear someone talk about an energy crisis, renewable energy or wasting energy, you can correct them, our energy is not running out, instead, we are just running out of easy sources of it.

Anyway, I hope this cleared up any misconceptions you had about energy, and helped you understand one of the most important physical aspects of the universe. Thank you for reading.
Check out my last two posts: 
"We don't serve neutrinos in here!"...A neutrino walks into a bar - What are neutrinos and what is all the fuss about?
The Irregularity of Time <1.5/2> (You might want to check out the first post on this topic before this) - Why time isn't as constant as you think.

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