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last class we learned about energy.in general in its relationship to work.today we're going to learn the.mathematical definitions.of the three most important or most.common.energy types so these are gravitational.potential energy which we're going to.call.gpe elastic potential energy or epe.and kinetic energy or ke.so i'm going to start with gpe here.so this is gravitational.potential energy.or in other words gpe.so the way that the equation for.gravitational potential energy.was discovered or made is.also with work so if you guys remember.the equation for work.is force times distance force times.distance so.someone thought okay so if i grab a book.and i lift it up one meter.then how much force did i have to do to.to lift that book so the force that.we're talking about when we lift things.so if we have to lift an object up here.the force that we have to do is exactly.the same as the force that is fighting.against us.right to to lift the object so the force.that is fighting against us is actually.gravity.which is m times g right so the force.that we're going to have to make to lift.the book.um at a constant speed is exactly the.same force.so our lifting force will also be.m times g so when we lift that object.that book that ball whatever it is.to an object through a distance sorry a.distance.x or a distance um.h because this is going to be the height.through which we move the the object.then we can calculate the work using the.force that we had to make.and the distance that we lifted it.through so basically what we're going to.get.is that the work is equal to so the.force.the force is going to be m times g.m times g and the distance is going to.be that height that we lifted it.um in total how much height we lift it.in so.times that h and that actually became.the equation for gravitational potential.energy.because the work that you do to lift the.object.is exactly the same as the amount of.gravitational potential energy.that the object will acquire when it's.up there.so that's why it was important to learn.last class that.work is that transformation and energy.and the transformation.in energy is caused by work being done.so what we get is finally our result.is that gpe.is equal to m times g.times h.so that's the result.the equation for gpe so here just.as a reminder to have it in your notes m.is mass.in kilograms um.g is the acceleration due to gravity so.9.8 meters per second squared.and h is the height.in meters always in meters.if you have these three values in these.units kilograms.meters and meters per second squared.you're going to get your energy.the gpe in joules.um so this the unit is joules.or j yeah so.we could do an example so the example is.going to be.if you have um an object.with a mass of.8 kilograms.and it's at a height at a height.of two meters.at a height of two meters.what is its gpe how much gravitational.potential energy does it have.so in your calculator you put.m which is 8 times g.which is 9.8 times 2.um which is the height and you're going.to get.156.8.so the gpa is the mass of 8.times the the g of 9.8.times the height of 2 which gave me.156.8.joules that's the example of gp.so that's it that's that's the simplest.equation.um gravitational potential energy okay.the following one.is elastic potential energy.so let me divide here.elastic potential energy.potential energy or as we're going to.call it.epe.so elastics are always talking about.something that.you deform with a force it requires a.force to deform it.to compress or to elongate the.the original length and.when you let go it's going to go back to.its original length.so the example that we always put here.is a spring so you have i don't know.suppose this is a wall.and you tied to it a spring.and tied to the spring is a box or.whatever right so that is the original.length.so when when nothing is touching it when.nothing when nothing is doing a force on.it.um the box is going to be.here in this position that we're going.to call.x equals zero zero meters.because that's where it is when there.are no forces acting on it.but you can either apply a force to.elongate the spring.which will move the the box.maybe i don't know out here.um or you can use your force to compress.the spring.and that will make the box be back here.right so that's going to be a different.x suppose that you.elongated it all of this distance.this is going to be your new x maybe.this is i don't know 2 meters.or maybe you compressed it.by x equals negative one meter.yeah so how much you move it is what we.call the compression or the elongation.of the spring that's going to be in the.equation.and the other thing that is in the.equation that we saw when we.saw hooke's law of spring force.last year at the end of last year was.the spring constant.so there is a constant of this spring.that we call k.that determines how hard how stiff it is.how hard it is.to compress or to elongate that spring.so we have basically two values here we.have.k which is called the spring constant or.the spring.stiffness constant stiffness.constant because it say how it says how.stiff.the the spring is to elongate or to.compress.and rx which is the elongation or.compression.so usually it's positive if we.elongate it and it's negatively.compresses.so we call it the elegation.because that's the one that's going to.be positive so compressing is.the opposite or the negative of.elongation so.how much you move it from that x equals.zero position.which is where it would normally be um.the hooke's law equation we saw it last.last year sorry and it depended linearly.on the elongation the equation was f.equals negative kx.we're not going to to use that one.right now but it is similar to the.equation for elastic potential energy.so let me write it in the same color.our equation is actually e p e equals.one half times the k.the spring constant times x squared.so you need to remember the one half and.remember the squared every time you do a.calculation.for elastic potential energy so that.would be.the resultant equation.so we can try an example just like.before.so i have a spring so we have a spring.of spring constant.k equals five and this the unit of the.constant is newtons.per meter um and you.you stretch.or elongate the spring.by um.two centimeters what is.the elastic potential energy so the.first thing is we need to remember.that the units are always the same.the s i units that we've been using.always so.our elevation has to be in meters.and our spring constant has to be in.newtons.per meter okay that's the only way that.we're going to get.the right unit for the energy in joules.so what we need to do is put it in the.in the equation but.just remember that these two centimeters.we have to convert them to meters.so epe would be.one half times rk which is 5.times the x squared which is.0.02 because we moved it twice.from centimeters to meters squared so.it's always going to be a pretty small.number.because usually you don't have springs.that you can elongate.a whole meter or a kilometer no you.usually just eliminate a spring.um a small amount in centimeters.so we put that into the calculator.so we're going to get one-half.times five times 0.02.squared gives me 0.001.oops 0.001.joules that would be the answer for the.example.i'm going to erase and do the last.equation.so the third and final energy that we're.going to look at today is kinetic energy.so we put it here kinetic.energy or as we call it.ke okay this one doesn't really have an.explanation.of where the equation comes from so i'm.just going to.go ahead and give you the equation and.you're going to see that it.looks very similar to that one so the.equation for kinetic energy.is one-half times the mass.m times the speed squared.this is the equation so notice that it.also has the one-half.just like elastic potential energy it.also has.a constant and it also has something.squared.in this case it's a distance in this.case it's a.speed or velocity so this is what we.have.and we need to put our.um mass in kilograms.so this again is mass in kilograms just.like for gravitational potential energy.uh one-half and the v is the speed.in meters per second always in meters.per second if we use these two units.we're going to get.kinetic energy in joules.oops joules.right so we can try an example it's.going to be basically very similar to.the previous example so we have.a ball of mass.um three kilograms ball.of mass three kilograms and it's moving.at um.let's say six meters per second.what is its kinetic energy.how much kinetic energy or how much.energy of motion does it have.so we just do the same thing we plug it.into the equation.so we've got kinetic energy equals.one-half.times the mass which is three times.the speed um squared so that's 6.squared don't forget the squared okay so.we put it in our calculators.one half times 3 times 6 squared and.that gives me.54. 54 joules.so that's it that's the way of.determining the energy that something.has thanks to its motion.so basically what you have to remember.is in gravitational potential energy it.has.more the higher up it is and the more.massive.it is in elastic potential energy it has.more energy the stiffer the spring is so.the harder it is to stretch or to.or to contract and the more.you elongate it the more you stretch it.the more energy is stored inside that.spring and for kinetic energy the more.massive the thing that's moving is and.the faster it's moving.the more energy it's going to have so.that's what you have to remember about.gp.ep and ke.

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DOE F 470 1 cdr U S Department Of Energy Energy FAQs

Here are some questions along with their answers to clear up the doubts that you might have.

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How does the U.S. Department of Energy work?

It's encouraged here as part of our culture. Follow the American dream! Have individualistic ideals. Be self starter and bussiness owner. In essence, in America, the patriotic capitalistic views are that there is nothing better than going from rags to riches, and trying and failing is better than never trying at all. And of course USA geopolitical position make sure it's clear citizen capable of such feats, so USA out invents because its part of the culture of rugged individualism and is economically feasible.

What does the U.S. Department of Energy suggest to curb Americans' energy use?

Problem: The primary barrier to progression in the energy efficiency marketplace is the current incentive system. Requiring people to reach into their wallet during tough economic times and wait while rebates are processed will not fill the market to capacity. In theory, rebates are meant to incentivize people to invest in energy efficiency, but in reality, customers are turned off by the process because it significantly lacks connectivity. Homeowners are eligible for a variety of different energy efficiency rebates at the local, regional and national level (all from different funding sources) Continue Reading

How does the U.S. Department of Energy affect the population?

In a nutshell, it is largely a combination of three things: the hangover from the end of the Cold War, 9/11 and the subsequent “War on Terror”, and the refusal of a number of countries to shoulder the burdens of preserving the global commons. When the Cold War ended & the Soviet Union collapsed, president George H.W. Bush assigned members of his administration, including James Baker & Dick Cheney, with the task of figuring out a new, post Cold-War foreign policy strategy for the United States going forward. Unfortunately, he lost his bid for re-election in 1992 and we elected a candidate with n Continue Reading

How can the U.S. Department of Energy be allowed to waste our tax money on the obvious folly of dark energy and matter?

If you can predict reliably which research will lead to direct benefits to our economy and society and which absolutely won’t — before the research is done, mind you — you should share that method with the rest of us. Otherwise you will have to put up with some research being judged (by yourself) as “wasted” after the research is done.

Why is the U.S. Department of Education always incorrectly referred to as DOE which is energy instead of its correct abbreviation which is DoEd?

Your question is a bit hyperbolic as the U.S. Department of Education is not always incorrectly referred to as DOE. While the official abbreviation is ED, people have a natural tendency to guess at the most likely abbreviation for any given entity rather looking it up, and DOE makes total sense if one is not aware that the U.S. Department of Energy also exists and officially utilizes the DOE abbreviation. I’ve most commonly used the abbreviations ED and DOE to refer to the U.S. agencies for Education and Energy respectively but I’d use the context in which an abbreviation was used to guess whic Continue Reading

As the electron in Bohr’s orbit of a hydrogen atom passes from state n =2 to n =1 , how does the kinetic energy (K) and the potential energy (U) change?

Using the Bohr’s atomic model :- K∝ 1 n 2 K∝1n2 U∝ 1 n 2 U∝1n2 So, when transition from n=2 n=2 to n=1 n=1 takes place, both the Kinetic energy and the Potential energy increase 4 fold.

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