Work and Energy (part 2) More on work. Introduction to Kinetic and Potential Energies.
Work and Energy (part 2)
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- Welcome back.
- In the last video, I showed you or hopefully, I did show
- you that if I apply a force of F to a stationary, an
- initially stationary object with mass m, and I apply that
- force for distance d, that that force times distance, the
- force times the distance that I'm pushing the object is
- equal to 1/2 mv squared, where m is the mass of the object,
- and v is the velocity of the object after pushing it for a
- distance of d.
- And we defined in that last video, we just
- said this is work.
- Force times distance by definition, is work.
- And 1/2 mv squared, I said this is called kinetic energy.
- And so, by definition, kinetic energy is the amount of work--
- and I mean this is the definition right here.
- It's the amount of work you need to put into an object or
- apply to an object to get it from rest
- to its current velocity.
- So its velocity over here.
- So let's just say I looked at an object here with mass m and
- it was moving with the velocity v.
- I would say well, this has a kinetic
- energy of 1/2 mv squared.
- And if the numbers are confusing you, let's say the
- mass was-- I don't know.
- Let's say this was a 5 kilogram object and it's
- moving at 7 meters per second.
- So I would say the kinetic energy of this object is going
- to be 5-- 1/2 times the mass times 5 times 7 squared, times
- velocity squared.
- It's times 49.
- So let's see.
- 1/2 times 49, that's a little under 25.
- So it'll be approximately 125 Newton meters, which is
- approximately-- and Newton meter is just
- a joule-- 125 joules.
- So this is if we actually put numbers in.
- And so when we immediately know this, even if we didn't
- know what happened, how did this object get to this speed?
- Let's say we didn't know that someone else had applied a
- force of m for a distance of d to this object, just by
- calculating its kinetic energy as 125 joules, we immediately
- know that that's the amount of work that was necessary.
- And we don't know if this is exactly how this object got to
- this velocity, but we know that that is the amount of
- work that was necessary to accelerate the object to this
- velocity of 7 meters per second.
- So let's give another example.
- And instead of this time just pushing something in a
- horizontal direction and accelerating it, I'm going to
- show you an example we're going to push something up,
- but its velocity really isn't going to change.
- Let's say I have a different situation, and we're on this
- planet, we're not in deep space.
- And I have a mass of m and I were to apply a force.
- So let's say the force that I apply is equal to mass times
- the acceleration of gravity.
- Mass times-- let's just call that gravity, right?
- 9.8 meters per second squared.
- And I were to apply this force for a distance of d upwards.
- Or instead of d, let's say h.
- H for height.
- So in this case, the force times the distance is equal
- to-- well the force is mass times the acceleration of
- gravity, right?
- And remember, I'm pushing with the acceleration of gravity
- upwards, while the acceleration of gravity is
- pulling downwards.
- So the force is mass times gravity, and I'm applying that
- for a distance of h, right?
- d is h.
- So the force is this.
- This is the force.
- And then the distance I'm applying is going to be h.
- And what's interesting is-- I mean if you want to think of
- an exact situation, imagine an elevator that is already
- moving because you would actually have to apply a force
- slightly larger than the acceleration of gravity just
- to get the object moving.
- But let's say that the object is
- already at constant velocity.
- Let's say it's an elevator.
- And it is just going up with a constant velocity.
- And let's say the mass of the elevator is-- I don't know--
- 10 kilograms. And it moves up with a constant velocity.
- It moves up 100 meters.
- So we know that the work done by whatever was pulling on
- this elevator, it probably was the tension in this wire that
- was pulling up on the elevator, but we know that the
- work done is the force necessary to pull up on it.
- Well that's just going to be the force of gravity.
- So we're assuming that the elevator's not
- accelerating, right?
- Because if the elevator was accelerating upwards, then the
- force applied to it would be more than
- the force of gravity.
- And if the elevator was accelerating downwards, or if
- it was slowing down upwards, then the force being applied
- would be less than the acceleration of gravity.
- But since the elevator is at a constant velocity moving up,
- we know that the force pulling upwards is completely equal to
- the force pulling downwards, right?
- No net force.
- Because gravity and this force are at the same level, so
- there's no change in velocity.
- I think I said that two times.
- So we know that this upward force is equal to
- the force of gravity.
- At least in magnitude in the opposite direction.
- So this is mg.
- So what's m? m is 10 kilograms. Times the
- acceleration of gravity.
- Let's say that's 9.8 meters per second squared.
- I'm not writing the units here, but we're all assuming
- kilograms and meters per second squared.
- And we're moving that for a distance of 100 meters.
- So how much work was put into this elevator, or into this
- object-- it doesn't have to be an elevator-- by whatever
- force that was essentially pushing up on it or
- pulling up on it?
- And so, let's see.
- This would be 98 times 100.
- So it's 9,800 Newton meters or 9,800 joules.
- After we've moved up 100 meters, notice there's no
- change in velocity.
- So the question is, where did all that work get
- put into the object?
- And the answer here is, is that the work got transferred
- to something called potential energy.
- And potential energy is defined as-- well,
- gravitational potential energy.
- We'll work with other types of potential energy later with
- springs and things.
- Potential energy is defined as mass times the force of
- gravity times the height that the object is at.
- And why is this called potential energy?
- Because at this point, the energy-- work had to be put
- into the object to get it to this-- in the case of
- gravitational potential energy, work had to be put
- into the object to get it to this height.
- But the object now, it's not moving or anything, so it
- doesn't have any kinetic energy.
- But it now has a lot of potential to do work.
- And what do I mean by potential to do work?
- Well after I move an object up 100 meters into the air,
- what's its potential to do work?
- Well, I could just let go of it and have no outside force
- other than gravity.
- The gravity will still be there.
- And because of gravity, the object will come down and be
- at a very, very fast velocity when it lands.
- And maybe I could apply this to some machine or something,
- and this thing could do work.
- And if that's a little confusing, let
- me give you an example.
- It all works together with our--
- So let's say I have an object that is-- oh, I don't know-- a
- 1 kilogram object and we're on earth.
- And let's say that is 10 meters above the ground.
- So we know that its potential energy is equal to mass times
- gravitational acceleration times height.
- So mass is 1.
- Let's just say gravitational acceleration is 10 meters per
- second squared.
- Times 10 meters per second squared.
- Times 10 meters, which is the height.
- So it's approximately equal to 100 Newton meters, which is
- the same thing is 100 joules.
- Fair enough.
- And what do we know about this?
- We know that it would take about 100-- or exactly-- 100
- joules of work to get this object from the ground to this
- point up here.
- Now what we can do now is use our traditional kinematics
- formulas to figure out, well, if I just let this object go,
- how fast will it be when it hits the ground?
- And we could do that, but what I'll show you is
- even a faster way.
- And this is where all of the work and energy
- really becomes useful.
- We have something called the law of conservation of energy.
- It's that energy cannot be created or destroyed, it just
- gets transferred from one form to another.
- And there's some minor caveats to that.
- But for our purposes, we'll just stick with that.
- So in the situation where I just take the object and I let
- go up here, up here it has a ton of potential energy.
- And by the time it's down here, it has no potential
- energy because the height becomes 0, right?
- So here, potential energy is equal to 100 and here,
- potential energy is equal to 0.
- And so the natural question is-- I just told you the law
- of conservation of energy, but if you look at this example,
- all the potential energy just disappeared.
- And it looks like I'm running out of time, but what I'll
- show you in the next video is that that potential energy
- gets converted into another type of energy.
- And I think you might be able to guess what type that is
- because this object is going to be moving really fast right
- before it hits the ground.
- I'll see you in the next video.
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