00:03
Okay, so we have a problem here and the problem says that, you know, we have the earth and the moon, and then we have two boxes.
00:20
So an astronaut goes, so this is the art, so an astronaut goes from the art to the moon and places the same type of box on the moon like it is on the art.
00:36
Okay, so you have two boxes here.
00:42
You have two boxes here.
00:43
Each one of them has one gram of protons.
00:50
Each one of them has one gram of protons.
00:54
And remember, since these are protons, it means that they're positively charged.
01:00
So they have positive charges on them.
01:03
And because they have positive charges, the protons in the moon are going to repel the ones on the art and then the ones on the earth are going to repel the ones on the moon.
01:16
So you can have your own kind of like naming convention where you say this force right here is f moon on earth and then this other force right here is f on moon.
01:35
So that just means that you have these repels forces.
01:41
This happens a lot in electricity where if you have two positive charges, if they come close to each other, they're going to repel.
01:51
Or if you have two negative charges, if they come close to each other, they're also going to repel.
01:58
So because they're like charges.
02:01
So like charges repel.
02:05
Like charges repel.
02:07
And then unlike charges, if you have a positive and a negative, unlike charges attract each other.
02:15
Okay? unlike charges attract each other.
02:18
So in our example, remember, you have positive charges on, you know, one box is in the earth, it has positive charges.
02:26
The other boxes in the moon, it has negative charges.
02:30
They are connected by a light stream between them.
02:34
And because of the repulsion forces or the forces of repulsion, there's going to be a tension on the string.
02:44
Think about kids playing on the playground and they're doing like a tag of wall where there's a group of kids on the right side and then another group of kids on the left side and they're pulling away from each other.
02:57
That's the case in this problem.
03:01
It's just that we don't have actual physical contact like the two groups.
03:11
But in this case you know, you have the two repulsion forces.
03:15
There's a string.
03:16
It's very long.
03:17
Reason why they say it's long is because the distance between the earth and the moon happens to be 3 .84 times 10 to the 8 meters.
03:30
3 .84 times 10 to the 8 meters.
03:34
So that's the distance between these two boxes.
03:39
Okay, 3 .84 times 10 to the 8 meters.
03:49
So our initial goal, obviously, in this problem, is to compute the repulsion force between these two boxes.
03:59
The other thing is that we have to address the, whether or not the earth and the moon are going to have an impact on the...
04:12
And the repulsion force.
04:14
And then the last part of the problem, obviously, is that we have to compute the gravitational forces between these two boxes.
04:22
These boxes have protons inside of them.
04:24
The protons are positively charged.
04:26
So when you think about kulom's law, so kulom's law is used in electricity, where charges and forces are involved.
04:36
So kulom's law simply said that if you wanted to compute the force of attraction or repulsion, between two charged bodies, then it's equivalent to it's proportional, not equivalent.
04:49
It's proportional to the product of the two charges and inversely proportional to their distance squared.
04:59
So this distance between the earth and the moon happened to be 3 .84 times 10 to the 8 meters.
05:05
We can build a formula.
05:08
We can build a formula that says f equals to k k u1 q2 over r squared and then notice that k is the constant the electric constant k happens to be the electric constant and k has a value also so k also has a value so in this problem we already have k we have r squared k the electric constant happens to be equivalent to one of a 4 pi e not if you want to compute that using the long method and that happens to be 9 8 .8 .988 times times 10 to the 9 newton meter squared of a of a cologne squared so so, you know, we have the value of k.
06:19
We also have the value of r, which is the distance between the two.
06:22
Remember, one is in the earth, the other one is in the moon, and so they're kind of like repelling each other.
06:28
And so we want to compute that force between them.
06:31
This force is going to be equal to the tension.
06:35
And that force also, it's the force of the repulsion force from the moon to the earth or from the earth to the moon based on the the the protons inside of the boxes so in the next page we're gonna see how all these numbers come together so f which is the tension we're looking for equals to k q1 q2 of a of our square we do we already have the value of k and we also have the value of r now we have to find the total charge inside of the boxes so to find the total charge inside of the boxes we have to find the number of protons inside the boxes times the charge of each proton remember the charge of each proton is 1 .6 times 10 to the negative 19 columns it's a positive charge because you're dealing with proteins.
07:52
Both protons and electrons have the same charge in terms of magnitude, but they have opposite signs, with electrons being negative and then protons being positive.
08:03
So in this problem, both cues are going to be positive anyways.
08:07
To find the number of protons inside of each box, you have to recall that each box has a bunch of proteins and has a mass of one gram, has a mass of one gram.
08:28
The mass of a single proton, the mass of a single proton, which you can call mp or mpr, happens to be equal to one point.
08:48
So this is just the mass of a single proton.
08:50
1 .6 -7 -262171 times 10 to the negative 27 kilograms.
09:06
That's the mass of a single parton.
09:09
You can change that to grams by multiplying by this by 1 ,000 grams over 1 kilogram.
09:19
And that happens to give us 1 .67262171 times 10 to the negative 24 grams.
09:29
You know, i guess you're thinking, why do we need the mass of a single proton? we need the mass of a single proton because if i have one gram equivalent of proteins and i know the mass of a single proton, it means that i'll be able to get the number of so to get the number of protons, we take 1 gram times 1 proton over 1 .67 -262171 times 10 to the negative 24 grams.
10:06
That's going to help us get the total number of protons that you're dealing with in this problem.
10:12
It happens to be 0 .5978.
10:19
5978 times 10 to the 24 proteins times 10 to the 24 proteins so you know we're on the right track our main focus is to end up solving for this formula right here we do have certain numbers in that formula we have the electric constant which is k and that happens to be 8 .98 times 10 to the newton meter squared over colom squared.
10:52
We also have the radius, the distance between the two boxes, which happened to be 3 .84 times 10 to the 8 meters.
11:00
We're only left with the charges.
11:03
Since we know the number of protons we're dealing with, we can take that 0 .978 times 10 to the 24 protons.
11:16
Okay.
11:17
And then you want to multiply by the single, charge of a proton, which is 1 .6 times 10 to the negative 19 cullums.
11:27
When you do that, you're going to end up with the total charge, the total charge in the boxes.
11:37
So we had the art and the moon, and we had boxes in the earth and boxes, a box, not boxes, a single box in the earth and the moon.
11:47
We want to get the tension between those two boxes.
11:49
This is qe and this is qm.
11:57
That's what we're looking for, the charge in the art and the moon.
12:01
When we multiply those two numbers, we end up getting 0 .95648 times 10 to the 5 kulams.
12:21
And a faster way of doing this is combining the, you know, 10 to the 24 and 10 to the negative 19.
12:31
And that gives us 10 to the 5.
12:33
And then you can use your calculator to multiply these two numbers.
12:37
There's 0 .5978 and the 1 .6 together.
12:41
And that gives you this number.
12:42
So now we have the charge.
12:44
We have all the numbers we're looking for.
12:47
So we can line them up and say k happens.
12:51
To be 8 .98, 988 times 10 to the 9.
13:01
Remember, care is the electric constant of a koulomb squared.
13:06
And then we have the value of the charges, both the charges on the earth and the moon.
13:12
And that happens to be 0 .95648 times 10 to the 5 columns.
13:24
And then the last thing you need is the distance between the two boxes on the earth and the moon, that's 3 .8 or 3 .84, times 10 to the 8 meters.
13:38
The next thing you're doing is you're applying the formula, which is the repulsion force between the protons.
13:47
So k, qe times qm over r squared, and this one becomes 8 .988.
13:58
Times 10 to the 9, newton meter squared over kulom squared, times 0 .9568 times 10 to the 5.
14:19
That's kulom's.
14:20
I'm going to square that because these two numbers are exactly the same.
14:25
Qe, which is the charge of photons or not, in the box or not, and qm, which is the charge of of protons in the moon, they're exactly the same.
14:36
So i'm just going to square that.
14:39
And then the radius is 3 .84 times 10 to the 8 meters squared.
14:46
And so the next step after that is the simplification process.
14:54
And there's an efficient way of doing it where you bunch up the floating numbers 8 .988 times 0 .95648 squared.
15:11
Remember it's squared.
15:12
Don't forget that.
15:17
And then over the 3 .84 also squared.
15:22
That's one part of the problem.
15:24
All i did was to take this one.
15:27
This one, take 8 .988 and then multiply to 0 .95648 squared and also.
15:34
Also 3 .84 squared.
15:36
You have to square this because of that exponent.
15:38
You have to square that because of the second exponent...