Gravitational Mass Bozeman Science English (auto-generated) English

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[Music] hi it's mr. Andersen and this is ap

physics essentials video 10 it's on

Hi. It's Mr. Andersen and this AP Physics essentials video 10. It is on gravitational

gravitational mass no name is as synonymous with gravity as Sir Isaac Newton who figured out that any two

mass. No name is as synonymous with gravity as Sir Isaac Newton who figured out that any

objects have a force between each other and that's that gravitational force and

two objects have a force between each other and that is that gravitational force. And

it's based on two things number one is the size of the two masses and then the

it is based on two things. Number is the size of the two masses. And then the second thing

second thing is as a square of the radius or the distance between their two centers of mass and so mass can be

is as a square of the radius, or the distance between their two centers of mass. And so

inertial mass like we learned in the last video inertial mass is based on

mass can be inertial mass, like we learned in the last video. Inertial mass is based

interactions between forces and objects it's best summarized by Newton's second

on interactions between forces and objects. It is best summarized by Newton's second law

law where if you apply a net force to an object it will accelerate and we can use

where if you apply a net force to an object it will accelerate and we can use that acceleration

that acceleration to calculate inertial mass gravitational mass is different it's an interaction between a mass and a

to calculate inertial mass. Gravitational mass is different. It is an interaction between

gravitational field such as the field that's produced around the earth and so

a mass and a gravitational field, such as the field that is produced around the earth.

that force down on that mass is equal to the gravitational mass and scientists

And so that force down on that mass is equal to the gravitational mass. And scientists

have noted something interesting that it doesn't matter what the mass is if an

have noted something interesting, that it does not matter what the mass is, if an object

object is in free fall it falls with the same exact acceleration and so

is in free fall it falls with the same exact acceleration. And so gravitational mass, as

gravitational mass as I said before is based on two things the mass of the two objects and note this that the force on

I said before, is based on two things. The mass of the two objects. And note this, that

object one and two are identical the earth pulls on you but you're also

the force on object one and two are identical, the earth pulls on you but you are also pulling

pulling on the earth and then the different the other thing is the radius between those two objects and so if we

on the earth. And then the other thing is the radius between those two objects. And

separate these two objects how could I make the force of attraction between the

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

two of them larger? Well I could just increase the mass of one of those objects and it is

objects and it's going to be a greater force on both of them how else could I

going to be a great force on both of them. How else could I increase the force between

increase the force between the two if I decrease that radius as I make this distance smaller the overall force is

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

going to become larger. So the closer it gets the greater that force is going to be. And

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

so what are some objects on our planet that are like that? An apple and the earth itself.

apple fall to earth it never really hit

And so why does an apple fall to earth? It never really hit Newton on the head, but he

Newton on the head but he was inspired by watching an apple fall it's because it's in a gravitational field and that

was inspired by watching an apple fall. It is because it is in a gravitational field

force is pulling the Apple down it's also what's holding all of us to the

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

planet right now. And so if I want to measure the gravitational mass, how do I do that?

I could use something like a balance how does a balance work you put a known

Well I could use something like a balance. How does a balance work? You put a known gravitational

gravitational mass on one side that's the kilogram and then we'll put an apple

mass on one side. That is the kilogram. And then we will put an apple on the other side

on the other side and we see how much it balances now I've never seen an apple that weighs 2 over 2 pounds maybe an

and we see how much it balances. Now I have never seen an apple that weighs over two pounds.

apple laptop and so we have to use a scale or rather a balance that's a

Maybe an Apple laptop. And so we have to use a scale or rather a balance that is a little

little bit different and so let's set it up like this we've got a known

bit different. And so let's set up it up like this. We have got a known gravitational mass

gravitational mass on this side 1 kilogram the Apple is not going to

on this side, 1 kilogram. The apple is not going to balance on this side. So we would

balance on this side so we'd have to move that point at which we're holding it over to the side so this starts to

have to move that point at which we are holding it over to the side. So this starts to resemble

resemble a triple beam balance for example and now we have it perfectly balanced the gravitational masses on

a triple beam balance for example. And now we have it perfectly balanced. The gravitational

either side of that pivot point are equal and so it's easy to figure out the

mass is on either side of that pivot point are equal. And so it is easy to figure out

mass of the Apple now we just measure the distance and the distance units are

the mass of the apple now. We just measure the distance. And the distant units are somewhat

somewhat arbitrary it could be in centimeters or inches it doesn't matter

arbitrary. It could be in centimeters or inches. It does not matter. As long as we are using

as long as we're using the same units on each side and now you simply solve like this and so on

the same units on each side. And now you simply solve like this. And so one the left side

on the left side we've got my mass 1 that's the mass of the Apple times the

we have got mass 1, that is the mass of the apple times the distance. In this case it

distance in this case it's going to be 10 on the right side we have the mass of the known mass the kilogram times the

is going to be 10. On the right side we have the mass of the known mass, the kilogram times

distance which is 1 and so I just plug in those values and then I solve for the

the distance which is 1. And so I just plug in those values and then I solve for the mass

mass of the Apple and it's going to be a tenth of a kilogram now a really good

of the apple. And it is going to be a tenth of a kilogram. Now a really good question

question might be could I take this balance to the moon and is it still going to read point 1 kilogram well the

might be could I take this balance to the moon? And is it still going to read 0.1 kilogram?

answer might surprise you you might think we'd bring it to the moon it's not

Well the answer might surprise you. You might think we bring it to the moon, it is not going

going to work anymore well it works exactly the same because on the moon

to work anymore. Well it works exactly the same. Because on the moon that gravitational

that gravitational force on the known kilogram is also going to be affected by

force on the known kilogram is also going to be affected by the gravity of the moon.

the gravity of the moon and so on the moon you're gonna measure the same exact gravitational mass now you might be

And so on the moon you are going to measure the same exact gravitational mass. Now you

confused if we were to look using a scale for example and talking about

might be confused. If we were using a scale, for example, and talking about weight, we

weight we'd find the weights going to change but gravitational mass is really

would find the weight is going to change. But gravitational mass is really a measure

a measure of how much material is in the object and therefore how much that

of how much material is in the object. And therefore how much that gravitational field

gravitational field is pulling on it and scientists have noted some interesting things on our planet going way back to

is pulling on it. And scientists have noted some interesting things on our planet going

Galileo who probably didn't drop objects

way back to Galileo who probably did not drop objects from the Leaning Tower of Pisa. But

from the Leaning Tower of Pisa but rather rolled these balls down an incline plane and varied the amount of mass and he

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

found that they all roll down with the same acceleration. And so Newton worked forward

forward with this using pendulums and even astronauts today are finding the

with this using pendulums. And even astronauts today are finding the same thing. So Dave

same thing so Dave Scott when he was on the Apollo 15 mission talks about

Scott, when we was on the Apollo 15 mission, talks about Galileo and this interesting fact.

Galileo in this interesting fact 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

"Well in my left hand I have feather. In my right hand a hammer. And I guess one of the

significant discovery about falling objects and gravity fields and we thought that it would be a better place

reasons we got here today was because of a gentleman named Galileo, a long time ago,

to confirm his findings on the moon and so we thought we'd try it here for you

who made a rather significant discovery about falling objects and gravity field. And we

and the feather happens to be appropriately a falcon feather for our Falcon and I'll drop the two of them

thought that where would be a better place to confirm his findings than on the moon?

here and hopefully they'll hit the ground at the same time

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

about that now if you were to try that

will hit the ground at the same time. How about that?" Now if you were to try that on

on our planet it's not going to work this only works in a vacuum otherwise

our planet it is not going to work. This only works in a vacuum. Otherwise air resistance

air resistance is going to affect it greatly and so did you learn how inertial mass which is based on the

is going to affect it greatly. And so did you learn how inertial mass, which is based

inertia of an object and can be measured using forces and acceleration differs

on the inertia of an object and can be measured using forces and acceleration differs from

from gravitational mass I hope so and I hope that was helpful [Music]

gravitational mass? I hope so. And I hope that was helpful.