# Energy: Important Facts

by Jared Rovny

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00:01 Let's summarize with some important facts that we've discussed about energy.

00:05 What we said is first, we have a kinetic energy which is equal to 1/2 the mass times the velocity of an object squared.

00:12 We introduce two different types of potential energy in this lecture.

00:15 We have the gravitational potential energy from an objects being in the air which it can unleash by letting go of the object and turning it into kinetic energy.

00:24 That gravitational potential energy was m times g times the height the object was from the zero of your coordinate system.

00:30 We introduce the spring potential energy, 1/2 k times the displacement of your spring from equilibrium square.

00:36 And then we said that the total energy which is conserved is equal to the kinetic plus the potential energy.

00:42 Now at this point, here we've introduced all of these variables with their different unit.

00:48 So it's a good idea to look at this, to think about them and make sure that you don't get confuse between each one.

00:53 We have our energy which is potential or kinetic or total.

00:57 And each one of these energies has units of joules because all energy always has unit of joules.

01:02 Now, we've now added this to sort of our, our set of variables that we have, including masses, velocities, heights and the spring constant which came to our potential energy equation for the spring.

01:14 One final note and this is something that many students get confused by and it's a common question.

01:19 If I say that the potential energy of an object is mass times gravity times the height of that object from the ground.

01:24 Could I just dig a hole below the object and then the new ground level would be a new zero below the object, sort of increasing the potential energy of the object, is that something we could do just by changing our ground level and digging a hole? The answer is no because the potential energy has nothing to do with the coordinate system that you've defined, so really what you're doing if you're digging a hole is not changing what the coordinate system is.

01:52 If you move your zero point from a one height to another all you've done is change your coordinate system.

01:57 So that's not really adding potential energy.

02:00 The number that you have for potential energy will change if you change the zero point of your coordinate system.

02:06 But potential energy does not care about its absolute value, the only time potential energy comes into a problem as the ones we've seen is with changes in height, changes in potential energy.

02:17 So for example, suppose I define two different coordinate systems.

02:20 On the left in the green, I have a coordinate system where I call the ground position equals 100 and you're always free to do this.

02:27 And then if I had a height of one, my new height would be 101.

02:32 In a different coordinate system, if I call the ground zero, a height of one would bring me to x equals 1.

02:37 In each of these cases, I have completely different coordinate systems and very different expressions for the potential energy of an object that was lifted to a particular height but the difference between my two locations, my ground in a particular height does not change.

02:52 And therefore the potential energy, the way that the potential energy changes and contributes to the kinetic energy, that won't change.

02:58 And again, so the potential energy it only cares about changes in potential energy because only if you change the potential energy converts some to kinetic energy for example, we get something physical.

03:08 And so keep this in mind, potential energy is relative, it's not absolute to a particular coordinate system and so feel free to always define any coordinate system you like because the fact that we've introduce potential energy expression of mgh does not mean that you have to pick the ground level to be zero for whatever problem you're doing.

03:27 So you can pick your coordinate system as long as you stick to it throughout the entirety of a problem.

03:32 So it's a long overview, what we have now is the Equations of motion, Newton's laws and Torque which is how we talked about force and we've just covered what energy is, both kinetic and a few types of potential as well as the total energy which is conserved when we haven't talked about energy lose to friction or anything like that.

03:50 We are going to discuss that now with Work, where Work is sort of the way that the energy changes when forces are acting on our object and so we'll discuss Work next followed by Momentum and that will finish our mechanic section at the beginning of this course.

04:03 Thanks for listening.

The lecture Energy: Important Facts by Jared Rovny is from the course Energy of Point Object Systems.

### Included Quiz Questions

1. E=3kx^2
2. E=1/2kx
3. E=mgx^2
4. E=mkx
5. E=kv^2
1. The mathematical value for potential energy will change if we change the coordinate system, but not the changes in potential energy from one point to another.
2. The mathematical value for potential energy cannot change, regardless of our coordinate system.
3. The potential energy of the object will increase, because of the energy we used in digging the hole.
4. The potential energy of the object will increase by the amount we have to use to hold it above the hole in the ground.
5. The changes in potential energy between locations will increase, but the mathematical value for the potential energy at any one point cannot change.
1. K∝v2, Ug∝h, Us∝(x-x0)2
2. K∝v2, Ug∝(x-x0), Us∝h2
3. K∝1/2v2, Ug∝g h, Us∝k2
4. K∝1/2v2, Ug∝mgh, Us∝1/2x
5. K∝mv2, Ug∝mgh, Us∝m(x-x0)

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