Hi. It's Mr. Andersen and this AP Physics essentials video 10. It is on gravitational
mass. No name is as synonymous with gravity as Sir Isaac Newton who figured out that any
two objects have a force between each other and that is that gravitational force. And
it is based on two things. Number is the size of the two masses. And then the second thing
is as a square of the radius, or the distance between their two centers of mass. And so
mass can be inertial mass, like we learned in the last video. Inertial mass is based
on interactions between forces and objects. It is best summarized by Newton's second law
where if you apply a net force to an object it will accelerate and we can use that acceleration
to calculate inertial mass. Gravitational mass is different. It is an interaction between
a mass and a gravitational field, such as the field that is produced around the earth.
And so that force down on that mass is equal to the gravitational mass. And scientists
have noted something interesting, that it does not matter what the mass is, if an object
is in free fall it falls with the same exact acceleration. And so gravitational mass, as
I said before, is based on two things. The mass of the two objects. And note this, that
the force on object one and two are identical, the earth pulls on you but you are also pulling
on the earth. And then the other thing is the radius between those two objects. And
so if we separate these two objects, how could I make the force of attraction between the
two of them larger? Well I could just increase the mass of one of those objects and it is
going to be a great force on both of them. How else could I increase the force between
the two? If I decrease that radius, as I make this distance smaller, the overall force is
going to become larger. So the closer it gets the greater that force is going to be. And
so what are some objects on our planet that are like that? An apple and the earth itself.
And so why does an apple fall to earth? It never really hit Newton on the head, but he
was inspired by watching an apple fall. It is because it is in a gravitational field
and that force is pulling the apple down. It is also what is holding all of us to the
planet right now. And so if I want to measure the gravitational mass, how do I do that?
Well I could use something like a balance. How does a balance work? You put a known gravitational
mass on one side. That is the kilogram. And then we will put an apple on the other side
and we see how much it balances. Now I have never seen an apple that weighs over two pounds.
Maybe an Apple laptop. And so we have to use a scale or rather a balance that is a little
bit different. And so let's set up it up like this. We have got a known gravitational mass
on this side, 1 kilogram. The apple is not going to balance on this side. So we would
have to move that point at which we are holding it over to the side. So this starts to resemble
a triple beam balance for example. And now we have it perfectly balanced. The gravitational
mass is on either side of that pivot point are equal. And so it is easy to figure out
the mass of the apple now. We just measure the distance. And the distant units are somewhat
arbitrary. It could be in centimeters or inches. It does not matter. As long as we are using
the same units on each side. And now you simply solve like this. And so one the left side
we have got mass 1, that is the mass of the apple times the distance. In this case it
is going to be 10. On the right side we have the mass of the known mass, the kilogram times
the distance which is 1. And so I just plug in those values and then I solve for the mass
of the apple. And it is going to be a tenth of a kilogram. Now a really good question
might be could I take this balance to the moon? And is it still going to read 0.1 kilogram?
Well the answer might surprise you. You might think we bring it to the moon, it is not going
to work anymore. Well it works exactly the same. Because on the moon that gravitational
force on the known kilogram is also going to be affected by the gravity of the moon.
And so on the moon you are going to measure the same exact gravitational mass. Now you
might be confused. If we were using a scale, for example, and talking about weight, we
would find the weight is going to change. But gravitational mass is really a measure
of how much material is in the object. And therefore how much that gravitational field
is pulling on it. And scientists have noted some interesting things on our planet going
way back to Galileo who probably did not drop objects from the Leaning Tower of Pisa. But
rather rolled these balls down an inclined plane and varied the amount of mass. And he
found that they all roll down with the same acceleration. And so Newton worked forward
with this using pendulums. And even astronauts today are finding the same thing. So Dave
Scott, when we was on the Apollo 15 mission, talks about Galileo and this interesting fact.
"Well in my left hand I have feather. In my right hand a hammer. And I guess one of the
reasons we got here today was because of a gentleman named Galileo, a long time ago,
who made a rather significant discovery about falling objects and gravity field. And we
thought that where would be a better place to confirm his findings than on the moon?
And so we though we would try it here for you. And the feather happens to be appropriately
a falcon feather for our falcon. And I'll drop the two of them here and hopefully they
will hit the ground at the same time. How about that?" Now if you were to try that on
our planet it is not going to work. This only works in a vacuum. Otherwise air resistance
is going to affect it greatly. And so did you learn how inertial mass, which is based
on the inertia of an object and can be measured using forces and acceleration differs from
gravitational mass? I hope so. And I hope that was helpful.