Hi. It’s Mr. Andersen and this is AP Physics essentials video 64. It is on work and energy.
And a track event that gets at the relationship between energy and work is the pole vault.
And the world record holder in the women’s pole vault is Elena Isinbeava. And that record
is sixteen feet seven inches. So what does that mean? If I were to stand on a basketball
rim she would be able to pole vault a half of a foot over my head which is pretty crazy.
I am sure it feels amazing to get over that bar. But it is really a physics question.
As she runs down the runway she is increasing her kinetic energy. She is then storing that
in the elastic potential energy of the pole. And then she is converting that into gravitational
potential energy. And so that pole is doing work. It is applying a force over a given
distance. And those are all going to be equivalent. The amount of energy she stores on the runway
is going to be the amount of potential energy she has at the top. And so in a system we
can add or pull out mechanical energy. And that could either be potential due to its
position or kinetic energy. But as we do that we have to move that system a certain amount
of distance. There has to be displacement. And that displacement is caused by an unequal
parallel force. In other words the parallel force has to be in the direction of that displacement.
And so since we have a force and a displacement, what are we talking about here? We now have
work. And work and that mechanical energy that is added are going to be equivalent.
And a nice tool that we can use in physics to look at how much work are we doing is to
look at a force versus displacement graph. And so let’s say we apply a constant force,
a parallel force, and we get a certain displacement, all we do is look at the area under that curve
and that is going to tell us how much work we have done and therefore how much mechanical
energy we have added to that system. Now let’s say it is not straight. Let’s say the amount
of force varies over time. It is still going to be the amount of area underneath that curve.
And since we are not using calculus in AP Physics we could just break this into all
of these different parts. We could figure out the amount of work and then the amount
of energy that has been added to that system. And so let’s give you an example of a problem.
Let’s say we have a bus that has a huge mass and we are applying a 12,000 newton force
to it. And that newton force gets an acceleration, since it is constant and moves a displacement
of 48 meters. So if we want to figure out how much work is done on that bus, work is
going to be equal to the force, F, times s. s is going to be the displacement of the object.
And so all we really need to know is what is that force and what is the displacement.
And so if I plug in those two values right here, it is that 12,000 newton force, times
a 48 meter displacement, and so the amount of work that we have done is going to be around
580,000 joules as we solve this for correct significant digits. So we have done that much
work on the bus. And so I will put that right up here. Now work and energy are going to
be equivalent. And so we have added energy to that system. We have added kinetic energy
to that system. And so the amount of work is going to equal the amount of kinetic energy
that we have added. And so how much kinetic energy did we have at the beginning? Well
the bus was at rest so there was zero amount of kinetic energy. And we have done work on
that bus and we have converted into all of that kinetic energy that we have at the end.
And so what makes this nice is once I know the amount of work I could figure out the
amount of kinetic energy assuming we did not lose a lot to friction. I could therefore
even figure out the velocity of that bus. So let’s do that. The amount of work, which
we calculated before, is equal to 1/2 m v squared. Again that is that final kinetic
energy. We know the mass of the bus, so we can just plug that in. It is 6,500 kilograms.
And then we can simply solve for v. We can solve for that final velocity of the bus.
So if I do that, I get a velocity of around 13 meters per second. And so it started at
0. Ends up at 13 meters per second. So it is going around 30 miles per hour at the end.
And so we are able to use this work-energy theorem or this work-energy relationship to
figure out once we have work we could figure out the amount of mechanical energy that has
been added. Now let’s give you a similar problem. This is a 12,000 newton force. But
let’s say a giant is pulling this bus. And it is at a 38 degree angle. So how would you
solve this one? Remember going back to that early concept map, that force has to be parallel
to the displacement. And so you would have to use a little bit of trigonometry. So you
would set it up like this. So this is going to be our adjacent side. So this is the x
value that we are looking for here. And so you are going to use the cosine of 38 equal
to that x over that force. And then you would figure out the force parallel to that movement.
And that is going to tell you how much work is being done. And so again a really nice
tool to get at this is a force versus displacement graph. And so what we have is force on the
side and then displacement along the bottom. So let’s say we have this object, a 3 kilogram
block. And we are going to apply the following forces to it. Let’s say we apply a constant
force to the right, a 30 newton force for the first 4 meters. And then we lessen that
force down to 0 over the next three meters. And so if I want to calculate how much work
is being done on that block, I am going to figure out the area under the curve. And so
I would start with this area right here. So how much work is being done? Well you just
figure out the area of this block right here. And so it is a force of 30 newtons. What is
our displacement? We would read that across the bottom. It is going to be 4 meters. And
so the amount of work that we are doing is going to 128 joules. It is just base times
height. And so that is how much energy that would block would have at the end. What kind
of energy is it going to be? It is going to be kinetic energy. Now watch what happens
after that. We are lessening the force down to zero. And so how do I figure out the area
there? Well that is simply a triangle. And so I could figure out what my base is. It
is going to be 3 meters. What is the force? Well, if we say this is a rectangle it is
1/2 base time height. It would still be 30 on this side times the displacement of 3.
So that would be 90 joules. But since we are 1/2 base times height I am going to get 45
joules. And so you can always calculate the area under a force displacement graph. That
is going to tell you not only the amount of work that has been done but the amount of
energy that has been added to that system. And so did you learn to make predictions about
changes in mechanical energy? Again, we have to make sure that that force is a parallel
force to displacement. And then finally could you apply the concepts of conservation of
energy? We are not losing energy. And this whole idea of work energy theorem to figure
out for example the velocity of that bus at the end? I hope so. And I hope that was helpful.