hey my name is kaeleigh and in this lesson we will discover how gravity acts as a
force it will be helpful if you've completed the modules for Newton's laws
and watched the what is gravity video let's get started gravity is an
invisible force we can't see it working but we feel it working every day it's
what brings us back down to earth after we jump and it keeps the moon in orbit
around the earth it's a very powerful invisible force gravity is the force of
attraction between any two objects with mass when an Apple falls from a tree the
earth pulls on the Apple but the Apple also pulls on the earth they are
attracted to each other this is the equation that describes the
attraction between two objects with mass that are some distance apart
it's called the law of universal gravitation if we go back to this
example of gravity with the Apple M 1 is the mass of the first object like the
Apple and M 2 is the mass of the second object like the earth and D is the
distance between them the big G is a constant it's called the gravitational
constant and even though it's a long number it's actually very small that's
what the 10 raised to a negative 11 exponent means a very small number
looking at this equation can you see how the masses of the objects and their
distance can change the gravitational force that they feel if the distance
between the objects is increased or larger
the gravitational attraction between the objects is less so objects that are
farther apart experience less gravitational attraction and if one of
the masses gets larger the attraction between the objects will increase but if
the object's masses decrease then the attraction between the objects will be
less do you want to try this equation in an example let's do it together
you and your friend both have a mass of 70 kilograms
you are standing one meter apart what is the force of gravitational attraction
between you both so let's write down what we know we know your mass is 70
kilograms and your friend's mass is also 70 kilograms so that's m1 and m2 and we
know the distance between you is 1 meter so that's Big D now we can write out our
equation so the gravitational force between U is equal to big G multiplied
by your mass multiplied by your friend's mass divided by the distance squared
between you both let's plug in our variables so if we plug in your masses
and the distance and we do the calculation you can definitely use a
calculator for these big numbers but you see that our answer is a number that is
so small 10 to the negative 7 that you wouldn't even notice the attraction
between you and your friend because that 10 to the negative 7 we can rewrite a
negative exponent as a tiny decimal that would look like this
so we'd move the decimal over 7 places so now there's six zeroes in front of
that 3 and that's the gravitational force between you and your friend and
that makes sense right you don't physically feel pulled towards your
friends which is a good thing tell em make playing
or hide-and-go-seek much more difficult and way less fun let's try one more
example together you have a mass of 50 kilograms and you are standing on earth
what is the Earth's attraction to you the mass of the earth is five point nine
seven times ten to twenty four kilograms and the radius of the earth is six point
three seven times ten to the six meters so let's write down what we know we know
that your mass is 50 kilograms and it also gives us the mass of the earth and
the distance between you and the center of the earth which let the radius of the
earth means and then we have our equation here so we can plug in our
variables and we get this long looking mathematical equation so definitely feel
free on these equations to use a calculator so you're gonna have
exponents in there and they can get a little confusing so just go slow plug
these numbers into your calculator make sure you use parenthesis where needed
and then when we press the equal button we will get 490 Newtons so we find that
Earth's gravitational attraction to you is 490 Newtons and that's when we round
to the nearest whole number now I want us to solve this same problem again but
we have another tool that we can use to solve this with much less math this
question is asking what the Earth's gravitational force is on you but this
is the same as asking how much do you weigh so we can solve this problem using
the equation we have for weight do you remember what that one is W equals M
times G where M is still your mass and G is the the little G the value of
acceleration due to gravity on earth so we can plug those numbers in now we just
have 50 times 9.8 and if we press the equal button on our calculators we get
490 Newtons and this is the same result we call pi using the universal law of
gravitation equation can you think of why in this example we can use either
the universal law of gravitation equation or the equation for weight it's
because of one little phrase you are standing on earth meaning you have
physical contact with the other object that has mass mass the earth your feet
are on the ground but the same idea applies when any object is exerting its
gravitational force onto a structure even like a heavy book resting on a
table now let's jump into the lab and take a look at how the universal law of
gravitation is affected by mass one mass two and the distance between them let's
play so here we are in our gravity force lab and you'll see I have two objects
and one the blue circle and M to the red circle and they both have masses that I
can control down here so the blue slider or the arrows control mass one and the
red sliders or the arrows control mass two and I also can pick up my guys here
and I can make them closer or farther apart okay so my variables within my law
of universal gravitation are mass one ms 2 and the distance between the objects
so a good thing to remember here with with these spheres is the distance
between these objects actually goes from this black dot right in the middle all
the way to this one in M 2 so it's so the center of the objects and up here
this little black arrow is representative of the force of
attraction they are feeling towards each other
that's also what this number here is you'll notice again that it's pretty
little there's a lot of zeroes in front of it but I also want you to notice that
this number is the same as this number so the force that they are being
attracted to each other is the same and now you can see how this form changes or
if those numbers are hard for you to make sense of we can unclick the show
values button I mean just pay attention to these arrows still representative of
the size of the force so let's see what do you think will happen if I increase
the blue ball mass so if one mass goes up does the attraction force increase or
decrease make your predictions and I'm increasing mass 1 and it looks like
those arrows are quite a bit bigger these guys are gonna have to pull a lot
harder to keep them from going towards each other so let's take mass 1 back
down how about right here and what's gonna happen if I move em 2 away from em
1 so if I'm increasing the distance between the Centers what will happen to
this force arrow I think it'll get smaller right so as
I'm moving away from the the objects away from each other these arrows got
smaller so now you get a chance you can play around these you can move them
around see what happens to the arrows change the masses try to make these
arrows as big as possible or as small as possible and see how mass and distance
effect the gravitational attraction between two objects alright have fun and
remember to always be clever