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Lecture Comments (6)

1 answer

Last reply by: Professor Dan Fullerton
Fri Jun 17, 2016 12:20 PM

Post by Hitendrakumar Patel on June 17 at 12:18:38 PM

A gulf ball is given 115J of energy by a club that exerts force over a distance.... How do we identify if we have to use the energy formula, kenetic energy formula or the gravitational potential energy formula? Or do we just assume we use the energy formula because no specific energy is given?

1 answer

Last reply by: Professor Dan Fullerton
Wed May 18, 2016 8:59 PM

Post by El Einstein on May 18 at 07:18:21 PM

For example 1. Is the answer to the correct significant figures?

1 answer

Last reply by: Professor Dan Fullerton
Thu Dec 11, 2014 9:02 AM

Post by melinda galacgac on December 10, 2014

How would i solve "A spring has K = 88N/m. use a graph to determine the work needed to stretch it from x=3.8 cm  to x=5.8 cm, where x is the displacement from its unstretched  length." i dont know to plug this into the formula

Energy

  • Energy is transferred by doing work.
  • The energy of a system includes its kinetic energy, potential energy, and internal energy.
  • A single object can only have kinetic energy, since potential energy requires an interaction between two or more objects.
  • Changes in a system’s internal structure can result in changes in internal energy.
  • Potential energy exists within a system if the objects within that system interact with conservative forces.

Energy

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Objectives 0:07
  • What is Energy? 0:24
    • The Ability or Capacity to do Work
    • The Ability or Capacity to Move an Object
  • Types of Energy 0:39
  • Energy Transformations 2:07
    • Transfer Energy by Doing Work
    • Work-Energy Theorem
  • Units of Energy 2:51
  • Kinetic Energy 3:08
    • Energy of Motion
    • Ability or Capacity of a Moving Object to Move Another Object
    • A Single Object Can Only Have Kinetic Energy
  • Example 1: Kinetic Energy of a Motorcycle 5:08
  • Potential Energy 5:59
    • Energy An Object Possesses
    • Gravitational Potential Energy
    • Elastic Potential Energy
  • Internal Energy 10:16
    • Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration
  • Calculating Gravitational Potential Energy in a Constant Gravitational Field 10:57
  • Sources of Energy on Earth 12:41
  • Example 2: Potential Energy 13:41
  • Example 3: Energy of a System 14:40
  • Example 4: Kinetic and Potential Energy 15:36
  • Example 5: Pendulum 16:55

Transcription: Energy

Hi folks! I am Dan Fullerton and I am thrilled to welcome you back to Educator.com.0000

Today's lesson is on energy.0004

Our objectives or goals are going to be to calculate the kinetic energy of a moving object, to calculate the gravitational potential energy of a system, and to analyze the relationship between the work done on or by a system and the energy gained or lost by that system.0007

So with that let us dive right in.0021

What is energy? From a physics' perspective, energy is the ability or capacity to do work, but if you remember, work is the process of moving an object.0024

So energy is really the ability or capacity to move an object.0034

Now there are lots of types of energy and a bunch of different ways we can break these up, but just as a starting point and a very, very, very strong oversimplification, we are going to say that all energy is broken up into either potential or kinetic...0039

...where potential energy is energy due to condition or position -- things like gravitational energy, where the amount of energy you have depends on how far you are from another mass.0054

Chemical energy is having to do with the energy involved in your bonds.0065

Elastic energy is energy due to how much a spring or something like a spring is compressed or stretched.0069

Electrical energy is where we have to deal with electric potential difference and we will get to that in a little bit, that is a lot of fun.0076

Nuclear potential energy... 0082

Kinetic energy on the other hand, is energy of motion, having to do with the movement or velocity of an object.0084

Electrical energy -- you will notice -- is in both places because over here we have moving electrical charges.0092

Light -- and this is a big oversimplification -- moving photons; wind -- moving air molecules; thermal...0098

Thermal energy is the energy caused by the vibration of the molecules or atoms making up an object, or sound, again vibrating air molecules.0106

So, types of energy -- we are going to break down into these two main types, potential or kinetic.0115

Energy of condition or position over here on the potential side, and energy of motion over here on the kinetic side.0120

Energy can be transformed from one type to another, and you can transfer energy from one object to another.0128

The way you transfer energy from one object to another is by doing work.0134

So the Work-Energy Theorem is going to be a big part of the course.0139

The work done on a system by an external force changes the energy of a system.0143

If I take the pen -- if I apply a force on it, if I do work on the pen, I am going to give it energy.0149

If I do work sideways on the pen, I am going to give it kinetic energy; it is going to go flying that way.0155

If I do work on the pen in this direction, I am changing its gravitational potential energy, but when I do work on an object, I transfer energy.0160

That is the Work-Energy Theorem in a nutshell.0168

The units of energy are the same as the units of work.0172

They must be because if I do work on an object, I am giving it energy.0174

They are two sides of the same coin.0179

The units are going to be joules (J), therefore, where a joule is a newton-meter (N-m), or 1 kg-m2/s2.0181

Let us start with kinetic energy as we dive into these in more detail.0189

Kinetic energy is energy of motion.0193

If energy is the ability or capacity to move an object, kinetic energy is the ability or capacity of a moving object to move another object.0196

Say a baseball is coming toward your nose at a 100 mph. It has a lot of kinetic energy.0207

It has a lot of kinetic energy because when that baseball hits your nose, it has a lot of ability to move another object, namely your nose.0212

It might not be pleasant, but it is going to transfer energy; it is going to do work on your nose and cause motion there.0220

The ability or capacity of a moving object to move another object is kinetic energy.0226

Translational kinetic energy -- we can quantify as 1/2 times the mass of the object times the square of the velocity.0231

Larger objects have more kinetic energy and faster moving objects have more kinetic energy.0239

If you are standing out on the road, do you want to get hit by a mosquito coming at you at 1 mph or 1 m/s, or do you want to get hit by a Mack Truck coming at you at 100 km/h, 60 mph.0245

Well, unless you have a death wish, you are probably after the mosquito, a lot less unpleasant.0258

It has a smaller mass, a smaller velocity and therefore a smaller kinetic energy.0263

A smaller ability to do work on you, a smaller ability to move you.0267

In the rotational world -- and we talked a bit about this briefly already -- the kinetic energy is 1/2 times the moment of inertia, times the square of the angular velocity.0272

And we have talked already about how (m) and the (i) were equivalents from the translational to rotational world and velocity and angular velocity are equivalents there as well.0281

Now a single object all by itself isolated and lonely can only have kinetic energy.0292

Potential energy requires an interaction between objects.0298

You need at least two objects to have any type of potential energy.0302

Let us take a look at the kinetic energy of a motorcycle with a simple example.0309

A frog speeds along on its motorcycle -- a frog-sized motorcycle of course -- at a constant speed of 30 m/s.0312

If the mass of the frog and motorcycle is 5 kg, find the kinetic energy of the frog-motorcycle system.0320

Kinetic energy, KE or K, is 1/2mv2, so that is 1/2 times the mass (5 kg), times the square of the speed (302) -- 900 × 5 = 4500 × 1/2 = 2,250 and again our units of energy and work, joules (J).0326

Now potential energy is often times written as (PE) or sometimes you will see it abbreviated with a capital (U) and the AP tends to prefer the capital (U).0360

That is an energy an object possesses due to its position or condition.0370

Potential energy exists within a system if the objects in that system interact with conservative forces.0374

Gravitational potential energy (Ug) is the energy an object possesses because of its position in a gravitational field.0381

The pen right here, has some amount of potential energy because if I let go of it due to its position, it is going to accelerate downward, and as it does that, that potential energy is going to become kinetic energy as it goes faster and faster and faster until it will eventually hits you...0390

...it will probably make a little of noise, create just a little bit of heat and we are going to convert that energy into other types.0405

Elastic potential energy, on the other hand, (US), typically for spring, is the energy an object possesses due to its condition of being compressed or stretched.0411

We take a spring, we do work on it to compress it, we compress it more and more and more and more and more, and now it has a bunch of energy.0421

I know that because if I let go of it, it is going to have a tremendous ability to move another object, to do work on something else.0427

If I let go of it, it goes flinging off to the side.0434

It has a lot of elastic potential energy.0436

As we talk about gravitational potential energy -- In a constant gravitational field we have to worry mostly about relative changes in gravitational potential energy.0442

What we are going to call 0 energy is really just an arbitrary point.0453

If I were to drop the pen onto the table here, I would worry about this distance.0457

I would call the table an energy level of 0 and this some other energy level.0463

On the other hand, if I were to drop it off the edge of the table, I could call the top of the table some energy level and I could call the ground 0.0468

It is all arbitrary where you set 0 so we are going to worry about differences in gravitational potential energy, δUg, where that is going to be mass times the acceleration due to gravity times the height difference from your high point to the point you are calling 0.0476

Or you could write that if you would prefer as mg(δh) and that works if you are in a constant gravitational field.0492

More universally, however, things get a little bit more complicated where the potential energy due to gravity is minus the gravitational constant times the first mass times the second mass divided by (r).0500

What is that negative sign about?0513

When we are talking about the universal calculation of gravitational potential energy, we really need some reference point to call 0, to measure all things against.0516

And what we are going to do to try and find a 0-point that makes sense is we are going to say imagine you have an object infinitely far away from all other objects, so far away that there are no other forces that interact with it -- infinitely far away.0526

That is what we have to call 0.0540

Now if we bring that object, say it is way, way, way out there in space -- here is Earth.0542

We bring that object closer and closer and closer and closer and closer to Earth. 0547

As we do that, its gravitational potential energy must be changing because now it wants to go toward the earth.0551

If we add 0 a long, long, ways away, now it is kind of captured by Earth that wants to go toward it.0558

So the gravitational potential energy that we have talked about while it is here on Earth -- the universal gravitational potential energy is negative because it is captured by Earth's gravitational field.0564

It has a negative energy of -1,000,000 J, that means if we did 1,000,000 J of work on it, we could completely free it from Earth's gravitational field and get it back out to infinity.0576

That negative sign just has to do with that reference point that we set way out there at an infinite distance away where no other objects interact with it.0589

If we want to calculate elastic potential energy -- for a linear spring -- something that obeys Hooke's Law, the potential energy in a spring is 1/2 times that spring constant times the square of the displacement from the equilibrium position or the displacement from its happy position.0598

Internal energy of a system includes the kinetic energy of the objects that make up the system and the potential energy of the configuration of the objects that make up the system.0617

If we were looking here at just the pen, and saying just looking at the pen, right here as it sits right now, its internal energy... 0628

...We could characterize by taking and looking at the average kinetic energy of all of the molecules making up this pen as they vibrate if we looked at it with a really, really, good, good, good, good, tremendously amazing microscope.0634

Now a change in a system's internal structure can result in changes in internal energy.0650

And we will see how that works out as we go through a couple of examples.0655

If we want to calculate gravitational potential energy in a constant gravitational field, let us set a 10 kg box on the floor -- Floor, box (10 kg).0659

And what we are going to do here is we are going to set its current position to ground level as a reference point as 0.0672

So we are going to call that while it is on the ground, its gravitational potential energy right there is 0.0679

We have set an arbitrary 0 that is going to make sense to us.0686

Now if we want to come over and we want to do something with our box -- if we want to do something like take our 10 kg box and we want to bring it up there somewhere, some height difference (h) from the ground, well to do that, we have to do work on it to lift it up there, right?0690

The work that we do on it has to be the force times that displacement or in this case, the force that we have to overcome to lift it is its weight, the force of gravity on it.0709

So that is the gravitational force and its displacement is going to be (h).0722

Well the force of gravity -- if we are in a constant gravitational field -- the weight we can write as (mg), so that is going to be (mgh).0728

Therefore, the potential energy that we have given this must be (mgh) -- gravitational potential energy in lifting that up -- its mass times the acceleration due to gravity here on the surface of the Earth, we can round that to 10 m/s2 times the height which we have raised it.0739

Now, an important point -- the source of all energy on Earth is the conversion of mass into energy.0762

Ultimately that is where it all comes from.0768

Think of where you get your energy. 0771

The gas in your car. Where did the gas come from? Well, refineries from oil in the ground.0772

Where did the oil come from? Critters, plants, long, dead compressed under lots of pressure for a long, long, long time. 0779

Where do they get their energy? Well eating other things.0786

The sun -- Where did the sun get its energy?0789

The sun is a giant nuclear reaction; it is a conversion of mass into energy.0791

So a lot of energy from the sun, anything from the sun is conversion of mass into energy.0797

What is our other source of energy?0802

Well straight up nuclear energy which is a conversion of mass into energy.0803

So the source of all energy on Earth is the conversion of mass into energy. 0808

Mass and energy are intimately related.0812

You are going to explore that in more detail later on toward the end of the course as well.0815

So let us take a look now at another example where we look at potential energy.0822

The diagram here represents a 155N box on a ramp.0825

An applied force (F) causes the box to slide from point (A) to point (B).0830

What is the total amount of gravitational potential energy gained by the box?0835

Well right away this could be an intimidating problem until we think about what we really need to do in order to find its change in potential energy.0840

The change in potential energy here is just going to be (mgh), or δh if you prefer.0848

Mass and mg, its weight, is just a 155N, and the height it is raised to 1.8 m -- 155 × 1.8 is about 279 J.0857

Energy of a system -- Which situation describes a system with decreasing gravitational potential energy?0882

A girl stretching a horizontal spring -- as you stretch that spring you are going to be giving the spring more energy because when you let go it is going flinging back that way.0889

You are giving it the ability to cause motion. It cannot be that.0898

Two -- a bicyclist riding up a steep hill.0902

A bicyclist is doing a lot of work going up the hill, up the hill, gaining the gravitational potential energy. It cannot be that one. 0906

A rocket rising vertically from Earth goes up and up and up and up -- changes its height and the height gets bigger and bigger and bigger; it is gaining gravitational potential energy.0914

But a boy jumping down from a tree limb is converting gravitational potential energy into kinetic.0922

His gravitational potential energy is being used up, so our correct answer must be 4.0927

A hippopotamus is thrown vertically upward. Do not ask me why.0937

Which pair of graphs best represents the hippo's kinetic energy and gravitational potential energy as functions of its displacement while it rises? Key -- while it rises.0942

Well let us think about that.0954

We have our hippo -- something, maybe a superhero, throws the hippo up, hippo goes upward.0955

As the hippo is going up, it starts off with a lot of velocity so it must have a lot of kinetic energy initially, and as it goes higher and higher and higher, it slows down, slows down, slows down, slows down -- stops.0966

Had a lot of kinetic energy here, now it has gravitational potential energy.0976

So kinetic energy was high here, very low, 0 here.0982

Gravitational potential energy was low here on the ground, but it was high up here.0986

Which graph shows us that? Must be number 1.0991

Start off with a lot of kinetic energy and as you have more and more and more displacement, you get less kinetic energy.0995

Start off with very little potential energy and as you add more and more displacement, you convert to potential energy.1001

And the key here being this is only looking at while the hippo is rising.1007

Let us take a look at one last example.1014

A pendulum of mass (m) swings on a light string of length (L).1017

If the swing hanging directly down is set as the 0-point of gravitational potential energy or I should say if the pendulum hanging directly down, is the 0-point of gravitational potential energy, find the gravitational potential energy of the pendulum as a function of θ and (L).1021

This is going to require a little bit more thinking here I believe. 1039

Well, let us think about what is going on here. 1043

At the highest point here, it has gravitational potential energy. 1045

As it swings down, it all becomes kinetic energy. 1051

We are trying to find the gravitational potential energy of the pendulum in terms of θ and (L).1056

Well, we know the change in gravitational potential energy is going to be (mgh). 1061

The trick then is going to be finding out what this (h) is as it moves from its lowest point to its highest point. 1069

To do that we are going to have to analyze this with a little bit of Geometry and Trig. 1077

The first thing I do here is I take a look and notice -- this is (L), then this length, also must be (L). 1081

If I draw a straight line over to the center of the ball on my pendulum though, this length now is no longer (L), it has gotten a little bit shorter, so (h) is the difference between (L) and this red line. 1089

If we could find the length of that red line, which is the adjacent side of this right triangle, we would be golden. 1108

So let us see if we cannot do that. 1115

Theta is there and we know the co-sine -- we want to know the adjacent side -- we know the hypotenuse.1118

Cos(θ) is the adjacent side divided by the hypotenuse (L), therefore, the adjacent side must be equal to (L)cos(θ), so this is (L) cos(θ). 1125

What we really want to know is this distance here, that (h). 1146

(H) then must be the total length of our pendulum (L) minus this (L) cos(θ) or I could factor out the (L)'s and say that that is (L) times 1 minus the cos(θ)1151

Now when I go to put that back into my formula here for potential gravitational potential energy, UG = mg, and instead of (h) here I am going to put (L) times 1 minus the cos(θ). 1166

So there is the gravitational potential energy of our pendulum when it is over here at this point. 1186

Its weight times the length of the pendulum times 1 minus the cos(θ), which really is just giving you the height difference from its lowest point to its highest point. 1195

Hopefully, that gets you a good start on energy. 1205

We will talk more about that in our next presentation on conservation of energy. 1209

Thanks so much for your time and make it a great day!1212