- Good morning.
-Today, we are going to introduce another equation for the force of gravity or weight of an object.
Flipping Physics
- However before we do. Bobby, please remind us
What is the equation we already have for the force of gravity or weight of an object?
- Force of gravity equals m times g.
- Bobby, please remember to say what the variables mean not just their letters.
- Sorry.
Force of gravity equals mass times acceleration due to gravity.
- I'm going to add a subscript which has up until this point been assumed.
The force of gravity is equal to the mass of the object times the acceleration due to gravity.
In other words, this is the force of gravitational attraction
which exists between an object near the surface of a planet and the planet.
Typically for us, the planet is the earth and with the acceleration due to gravity
equal to nine point eight one meters per second squared.
In fact it turns out,
there is a force of gravitational attraction between any two objects.
The equation to determine this force of gravitational attraction between any
two objects is Newton's universal law of gravitation
And the equation is the force of gravity equals big G or the universal gravitational constant times the mass of
object 1 times the mass of object 2 all divided by r squared.
The universal gravitational constant or big G as I like to call it is an experimentally
Measured number and has an accepted value of six point six seven times 10 to the negative 11 Newton's
times meters squared over kilograms squared.
Mass one and mass two are the masses of the two objects which have the force of gravitational attraction
between the two of them.
And, now let's talk about the r in this equation
Please, class repeat after me r is NOT the radius.
-Class: r is NOT the radius.
- r is the distance between the centers of mass of the two objects.
Class: r is the distance between the centers the mass of the two objects.
- So, r is not defined as the radius.
The definition of r
Is that it is the distance between the centers of mass of the two objects.
This can be confusing because sometimes r actually works out to be the radius
However, r is not defined that way.
- r is not the radius, but sometimes it is the radius.
- Sure, r is not defined as the radius; however, there must be situations where r works out to be the radius
- I wish they used a different letter for r because that is confusing.
- Me too. - Yeah.
- I totally agree. Just so you know even though Sir Isaac Newton published his book Principia in
1687 which included his universal law of gravitation
Newton never actually was able to measure the universal gravitational constant with any real accuracy.
It wasn't until 1798 more than 100 years later
that a British scientist named Henry Cavendish performed the first accurate measurements of the universal gravitational constant
He used a large torsion balance to measure big G. The torsion balance had two stationary
350-pound lead balls and
suspended on a metal wire a six foot long horizontal wooden rod with two
1.6. Pound lead balls on either end of the wooden rod. The whole contraption was put in a large box and Henry
Cavendish used telescopes to observe this slight motion of the
21.6 pound lead balls toward the other
350 pound lead balls.
You know what, let's talk through some qualitative examples of Newton's universal law of gravitation.
Let's start with a completely empty universe. To be clear right now nothing exists in this universe.
Now let's add one can of dog food.
Notice because there is only one object in this universe
There is no force of gravitational attraction because it takes two objects,
mass 1 and mass 2 to have a force of gravity.
Without a second mass there is no force of gravity.
Now let's add a second can of dog food
Notice now each of these cans of dog food has a force of gravitational attraction pulling it towards the other one.
The force from can 1 on can 2 is pulling can 2 toward can 1. And the force from can 2 on can 1 is
pulling can 1 toward can 2.
Please realize these two forces form a Newton's third law force pair.
The force from can 1 on can 2 is
equal and opposite to the force from can 2 on can 1.
- If there is nothing else in this universe
Wouldn't the two cans of dog food accelerate towards one another?
- Bo, that is a valid point. Yes, the cans would accelerate towards one another.
However, right now I am just concerned about making sure you understand the forces.
So, let's let's not worry about the accelerations of the objects.
Now, let's add a third can. Bobby, what additional gravitational forces exist in this universe?
- Well, can one is pulled toward can three and can three is pulled toward can one.
Oh yeah, can two is pulled toward can three and can three is pulled toward can two.
- Correct, and let's add a fourth can.
Billy, what additional gravitational forces exist now in this universe?
- Well, can four interacts with the other three cans. So,
Cans one two and three are each pulled toward can four and
and can four is pulled toward cans one, two, and three. - That is correct.
Okay, let's be done adding cans of dog food to our universe.
- Mr. P. - Yes, Billy.
- Now that we have two equations for the force of gravity. How do we know which one to use?
- Yeah. - That is a fair question.
Bo, remind me the original force of gravity equation the force of gravity
equals the mass of the object times the acceleration due to gravity.
That is the force of gravitational attraction between
what two objects?
- That is the force of gravity between an object and the earth.
- Remember the object needs to be near the surface of the earth. If the object is in orbit, then that equation is not valid yeah
Class Agreed
- Correct, I prefer to realize we could be on a planet other than Earth and identify that this equation is a planet
specific equation. We can find the force of gravity or the weight of any object on a planet using this equation.
Newton's universal law of gravitation is always correct.
We can always use this equation to solve for the force of gravity which exists between any two objects
Which means we don't actually need the equation force of gravity equals object mass times acceleration due to gravity
However, in recognition that we often need to determine the weight of objects here on planet earth,
we have the shorter much easier to use equation
Thank you very much for learning with me today. I enjoyed learning with you.