Energy

Energy

the ability to do work

I’m gunna warn you right now, energy is a very abstract concept. Some times it seems like the guys who invented this stuff were just pulling it out of their ass. Maybe they did, but the bottom line is, energy is a very valuable tool. It can get you past some problems that there is no way to solve with any other method. However if your like most people and don’t give a damn how handy it is, just keep in mind your teacher is going to test you on this. So let’s get through it together.

Nuclear Power is safer than eating Peanut Butter! Energy is everywhere. You use electromagnetic energy to power your N64 and you use chemical energy to light a joint. We also used nuclear energy to give Chernobyl that pretty green glow. Better Dead Than Red! Just kidding! KGB no kill me.

There are tons of different kinds of energy. Fortunately we only need to talk about one right now. Mechanical energy. Mechanical energy deals with things in motion. Like all energy, it comes in two forms, kinetic and potential. Kinetic energy is the energy an object has because of its motion. Potential energy is the energy an object has because of its position. Let’s get into the details.

Kinetic Energy

the ability to cause you pain

Kinetic Energy Equals One Half Mass Velocity Squared

There it is. That’s the formula you need to find the kinetic energy of an object. So… what does it mean? Basically in words that means the more massive an object or the faster its moving, the less you want it to hit you (the more energy it has). An object with a great deal of kinetic energy causes a great deal of pain if it hits you.

It’s kinda common sense hiding behind math. If a friend throws an innocent hamster at you at one meter per second, you are probably going to catch the little guy without much fear of injury. However if a cement truck (more mass) is coming at you at the same speed, you’re going to want to get out of the way. That makes sense right? Now if your friend throws that hamster at you at one hundred meters per second (increased velocity), there is no way your gunna try to catch the little guy. He’d tear right trough your hand. That’s kinetic energy.


Gravitational Potential Energy.

The ability to, maybe, cause you pain

Equals

Mass

Acceleration Due to Gravity 9.8 meters per second squared

Gravitational potential energy is a little weird. It says that an object has more energy if it is higher off the earth’s surface. The Gravitational potential energy it’s self doesn’t really do anything, hence the word potential (like when your parents yell at you to fulfill your academic potential). It kicks in when the object is allowed to fall. As the object falls, it’s gravitational potential is ‘converted’ into kinetic energy, and the object moves faster. Here is an example. You are not going to be concerned if a penny drops on your head from a height of one meter, (very low gravitational potential energy) but if it is dropped from one thousand meters, (very high gravitational potential energy) that’s gunna hurt.


The Work-Energy Theorem

Now that we know about work, kinetic energy, and potential energy, we can talk about the idea that links them all together, the work-energy theorem. Strictly speaking energy is the ability to do work. Objects with a lot of energy can move massive objects a short distance or less massive objects a larger distance. The work-energy theorem says that the amount of energy gained (or lost) by an object is equal to the amount of work done on the object. The gravatational potential energy an object gets is the same as the amount of work done to lift that object.

Mathematically we say W=Delta E. Work equals the change in energy. That’s all fine and good, but it’s not going to help us solve problems in that form. If we screw around enough with it we can get the more useful,

Work

Equals

Delta (Change In)

Kinetic Energy

Plus

Delta (Change In)

and the even more useful,

Work

Equals

Open Brackets

One Half

Mass

Final Velocity

Squared

One Half

Mass

Initial Velocity

Squared

Close Brackets

Plus

Open Brackets

Mass

Acceleration Due to Gravity 9.8 meters per second squared

Mass

Acceleration Due to Gravity 9.8 meters per second squared

Close Brackets

DON’T PANIC! Let me walk you through it.

The first equation and the second equation say exactly the same thing, only in a different way. If you look at it long enough, you may find the relationship by yourself. But I’m not going to wait around for you so here it is. Remember the formula for Kinetic energy?

Kinetic Energy

Equals

One Half

Mass

Velocity

Squared

How would we figure out the change in kinetic energy of an object? Well when we want to find the change in anything, it is the final value minus the initial value. So the final kinetic energy would be,

Kinetic Energy

Equals

One Half

Mass

Final Velocity

Squared

We leave the mass alone because it is safe to assume that it will not change. The initial kinetic energy would be,

Kinetic Energy

Equals

One Half

Mass

Initial Velocity

Squared

So the change in kinetic energy would be,

Now we can see where the first part of that long equation comes from. To get the second part we follow basically the same reasoning. The formula for gravitational potential energy is,

Equals

Mass

Acceleration Due to Gravity 9.8 meters per second squared

Vertical Displacement

So if we want to find the change in the gravitational potential energy of an object, we simple take the final value minus the initial value.

That is were we get the second part of the long equation. It seems much less intimidating now.

So what is this bad boy used for? Well, the kinetic energy plus the potential object is always going to be the same number. Always. For example, if you are given the total energy of an object, its mass and it’s height, you can find its velocity. First calculate the potential energy from the mass and height. Subtract that from the total energy, that gives you the kinetic energy. From there you can solve for the velocity.

Kinetic Energy Hamster

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