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PROF.
WALTER LEWIN: Let's do a simple example.
Applying this work energy theorem, I have an object that I want to move
from A to B. I let gravity do that.
I give it a velocity.
Here is the velocity v of A. And let the separation be h.
And this could be my increasing y direction.
The object has a mass, m.
And so there is a gravitational force, which is m*g.
And if I want to give it a vector notation, it's m*g y roof.
Because this is my increasing value of y.
PROF.
WALTER LEWIN: When it reaches point B, it comes to a halt.
And I'm going to ask you now, what is the value of h?
We've done that in the past in a different way.
Now we will do it purely based on the energy considerations.
So I can write down that the work that gravity is doing in going from A to B,
that work is clearly negative.
The force is in this direction, and the motion is in this direction.
So the work that gravity is doing in going from A to B equals - m*g*h.
That must be the kinetic energy at that point B, so that this kinetic
energy at point B minus the kinetic energy at point A, this is zero,
because it comes to a halt here.
And so you find that 1/2 m*(v_A)^2 = m*g*h.
m cancels, and so you'll find that the height that you reach
equals (v_A)^2 / (2g).
And this is something we've seen before.
It was easy for us to derive it in the past, but now we've done it purely
based on energy considerations.
I'd like to do a second example.
I lift an object from A to B. I, Walter Lewin.
I take it at A. It has no speed here.
v_A is zero.
It has no speed there.
And I bring it from here to here.
There's a gravitational force, m*g, in this direction, so the force by Walter
Lewin must be in this direction.
So the motion and my force are in the same direction.
So the work that I'm doing is clearly + m*g*h.
So the work that Walter Lewin is doing is + m*g*h when the object goes from A
to B.
The work that gravity was doing was - mgh, we just saw that.
So the net work that is done is zero.
And you see there is indeed no change in kinetic energy.
There was no kinetic energy here to start with, and there's no kinetic
energy there.
If I take my briefcase and I bring it up here, I've done positive work.
If I bring it down, I've done negative work.
If I bring it up, I do again positive work.
When I do positive work, gravity does negative work.
When I do negative work, like I do now, gravity does positive work.
And I can do that a whole day, and the net amount of work that I
have done is zero.
Positive work, negative work, positive work, negative work.
I will get very tired.
Don't confuse getting tired with doing work.
I would have done no work, and I would be very tired.
I think we would all agree that if I stand here 24 hours like this, that I
would get very tired.
I haven't done any work.
I might as well put it here and let the table just hold that
briefcase for me.
So it's clear that you can get very tired without having done any work.
So this is the way we define work in physics.