Hi. It's Mr. Andersen and this is AP Physics essentials video 35. It is on the contour
line, which is a line of equal elevation and therefore a line of equal gravitational potential
energy. Now this is really an earth science topic. So you might be asking yourself why
are we talking about this in physics. Well we are going to use this idea of contour lines
as an analogy to talk about equipotential lines in electric fields. So before we get
to that, and we will mostly get to that in the next video, take a look at this bowl.
We have a bowl that is inverted. And I want you to have an idea, a mental picture of how
this looks three-dimensionally. And so we have these steep sides like this and then
it is going to be relatively flat on top. So let me show you a quick activity I did
to draw the contour lines. So what I did was I put that bowl inside a little plastic tub.
I also put markings on the side of it. And so these are markings of equal distance up
the side. And I am going to add water to it. And now I am going to show you what this looks
like from above. So I took a picture directly above. And then with that white line what
I am marking is the bottom of this tub. I then added a certain amount of colored liquid.
And so I have added it to that first line. And now what I have done is traced where the
water is hitting the bowl. Because that is going to be a contour line, a line of equal
elevation. Then I added a little bit more water and I drew the next line. And the next
line. And the next line. And the next line. And the next line. You can see that it is
about to go under water. And then the last line like that. And so those are contour lines,
lines of equal elevation. And so what can we tell looking at those contour lines? Well
right at the bottom it was flat. But on the sides, when those contour lines are really
close together that means it is really steep. And that the top it is relatively flat. You
can see the table I was shooting this on was not perfectly flat, because one side of the
bowl is tipped up a little bit and that kind of eventually went under water. So that is
a contour line. And so if you ever have a scalar field, in other words a field where
we have a bunch of values like that, it is often times hard to make sense of that. And
so in the sciences what we do is we draw isolines, lines of equal scalar value. And on a topographical
map we call those contour lines. Those that show layers of equal elevation. And so we
can use that as a measure of gravitational potential energy. The farther you are away
from the center of the earth the more an object has a certain amount of gravitational potential
energy. And so when those lines are close together than it is going to be steep. And
when they are far apart it is going to be flat. Can you pick out something else about
these contour lines? Another rule is that they will never cross each other. You are
never going to have an area that is two elevations at the same time. And so that is why the contour
lines will never cross. And why are we learning about the earth science in physics? Remember
we are going to use it as an analogy for electrical equal potential lines. And we will get to
that more in the next video. And so before we get to that let's kind of go through the
specifics of a contour line. So what I have here is the bottom half of a hill. And so
you should be able to look at a contour line like this and start to build a three dimensional
picture of what that hill looks like. There are a couple of important things. We will
label important lines. So this is 100 meters. This is going to be 300 meters. Often times
on a topographic map you will see what is called the contour interval. That is going
to tell you the amount of elevation distance between each of these two. So if this is 100
you should know that this 150, 200, 250, and this is going to be 300 right here. But what
you can do is you can draw a topographic profile. So I have drawn a line right through the middle
of this hill. And we are going to project each of those elevations on to this grid above.
And so up here we have elevation on the y-axis. And then we are going to have distance on
the x-axis. And so you can simply plot each of those lines. And that is going to give
you a topographic profile of this hill. So what we can see is down here on the contour
lines, when they are really close together then we are seeing a really steep elevation.
And then on the other side it is going to be more gradual. It is going to have a lower
slope on that side. And so those are contour lines. If you take a look at this map, I mean
you may want to pause the video for a second and try to figure out what this looks like
three dimensionally. Again these contour lines are showing equal elevation and therefore
equal gravitational potential energy. And so you can see here that this would be 11,500
here. This is 3,500. And so do you have a three dimensional picture of what this looks
like? Well let me show you. So this a three dimensional map of this topographic map. And
so if I were to put an arrow right there, could you point on the three dimensional map
where that would be? Well it is starting in the lower left. You can see that these lines
are equally spaced. And so that is going to be just going right up this slope here. So
we have pretty much an equal slope right here. What would this be where they are all pointing
down? That would be this ridge line coming right down here. You can see where they are
pointed up, we are going up this little valley right here. You might think this is going
to be flat on the top. But again the elevation is getting higher in here and so this would
be right up here at the peak of that, right there. And so in a topographic map those contour
lines are going to show areas of equal elevation. But what we are going to do is use this as
an analogy in the next video. We will transfer towards electric equal potential lines. And
so if we have a positive and a negative charge, there are going to be electric fields around
that. And so these lines represent areas of equal potential. So over here in the topographic
map it is gravitational potential. But over here it is going to be electric potential.
And so did you learn to represent these contour lines as isolines? Lines of equal gravitational
energy? I hope so. And I hope that was helpful.