- Good morning. Bobby, please read the problem and Bo please translate
Flipping Physics
- According to NASA, the mass of the Earth is 5.97 x 1024 kg,
the mass of the Moon is 7.3 x 1022 kg,
and the mean distance between the Earth and the Moon is 3.84 x 108 m…
- Stop.
Mass of Earth is 5.97 x 10^24 kg and
mass of moon is 7.3 x 10^22 kg.
But I don't know what variable to use for the mean distance between the Earth and the moon
- Let’s use R with a subscript of E dash M.
- Okay, that equals 3.84 x 10^8 m. Bobby?
- What is the force of gravitational attraction between the Earth and the Moon?
- Force of gravity equals question mark.
- Billy, please solve the problem. - Well, we need to use Newton's universal law
of gravitation or the big G equation
force of gravity equals
the universal gravitational constant or big G times the mass of the Earth times the mass of the moon all divided
by the square of r
Which is the distance between the centers of mass of the two objects.
And then we get...
- Hold up Billy, let’s review that for just a second.
Class, r is not …? - Class: the radius.
- r is ... - Class: the distance between the centers of mass of the objects.
- This can be confusing because sometimes r is ...
- Class: the radius.
- Thanks. Billy, please continue.
- Sure, plugging in numbers gives us, 6.67 times 10 to the negative 11 times
5.97 times 10 to the 24th times 7.3 times ten to the 22nd
Mmm all divided by
Oh r is the mean distance between the Earth of the Moon so.....
divided by 3.84 times ten to the 8th squared
and that works out to be 1.97134 times ten to the 20th or
2.0 times 10 to the 20th Newtons with two significant digits.
- Great. Okay, remember
this is the force the Earth is applying on the Moon and the force the Moon is applying on the Earth.
So the Moon right now is being pulled towards the Earth with a force of 2.0 times ten to the 20th newtons.
Turns out, we can actually determine the acceleration of the Moon
which is caused by the Earth. The net force acting on the Moon from the Earth
equals the Force the Earth exerts on the Moon which equals the mass of the moon times the acceleration of the moon.
Therefore we can solve for the acceleration of the moon,
plug in numbers and get the acceleration of the moon towards the Earth to be roughly
0.0027 meters per second squared.
And notice that acceleration is a constant number; therefore
we can use a
uniformly accelerated motion equation to determine how long it is before the Moon crashes into the Earth
and destroys all life on the planet.
The displacement of the Moon, or the mean distance between the Earth and the Moon,
equals the velocity initial of the moon, which, relative to the Earth is zero, times change in time plus
one half times the acceleration of the moon times change in time squared.
We can plug in all the numbers and rearrange the equation to get
The change time in seconds, however, I think it would be much better expressed in days.
So. Roughly 6.2 days before the Moon slams into the Earth and pretty much
everything on the planet goes extinct
Good luck everybody. I think I'm gonna go spend my last six days with my family. Bye.
- That cannot be right. Can it? - I don’t think so.
- No way. That does not make sense. - Oh hey Raivat. How is India?
- Currently worried about the mass planetwide extinction due to a collision between the Earth and the Moon.
Otherwise, India is fine. Thanks.
- That’s good. - Actually, as the Moon moves towards the Earth the distance between the two will decrease, so the
Force of gravity will increase, so the acceleration is actually not uniform,
so we cannot use the uniformly accelerated motion equations.
- That just makes it worse
We all die sooner because the acceleration increases as the Earth and the Moon get closer to one another.
- There are a lot more forces acting on the moon than just the force of gravity caused by the Earth, right?
I mean, there’s the Sun, Mars, Venus, Jupiter.
- Right, but I think he's just considering the earth and the moon here. I mean the moon is in orbit around the earth
- That's it the moon is in orbit around the Earth. - Yeah. He did not identify the direction he summed the forces in.
He summed the forces in the in-direction; therefore the acceleration of the moon is a centripetal
acceleration. It is the acceleration which keeps the Moon moving in orbit around the Earth.
- The inertia of the Moon tries to keep it moving in a straight line and the centripetal acceleration
keeps it moving in a circle.
- The net force in the in-direction equals the force the Earth causes on the Moon,
therefore the force the Earth causes on the Moon is the net force in the
in-direction and is therefore the centripetal force which causes the Moon’s orbit.
- I get it.
We are all not going to die in six point two days
That's good
- But in in like seven billion years our Sun will expand into a red giant star and kill us all
- Right, but before that the sun will heat the earth up so much
we won't have any atmosphere left
and that will kill us all. - Did y’all notice the r in Newton’s Universal Law of Gravitation
actually did end up being the orbital radius of the moon
around the center of mass of the earth-moon system in this problem.
Huh, sometimes r is the radius.
- Thank you very much for learning with us today. We enjoyed learning with you.