Good day everybody, my name is Brad Langdell and I'm hoping this physics I'm talking to you about today is not going to seem like I'm just talking Greek to you Although we are going to talk about a Greek symbol the Greek symbol alpha And I want to introduce to you a type of problem called a proportionality problem is what we call them in our class I introduced these in unit B of physics 20. We do a unit C and D as well And you're going to recognize these types of problems when you're doing an assignment or a test because they're going to contain words like doubles Triples halves quarters increases or decreases by a factor of some amount So maybe increases by a factor of seven or decreases by a factor of four something like that You'll also notice that these types of problems don't often have a lot of numbers in them like you know mass is equal to five Kilograms or something like that. So when you see those keys, you know, you're going to be dealing with Proportionalities and we're going to use this cute little guy here to help us solve some of these problems So I just pulled out a question here Box has a weight of five new 500 Newtons on earth If the box is moved to a planet with a mass five times larger than the earth and a radius half as large Find a the mass of the box in the other planet and be the weight of the box in the other planet This is kind of a loaded question actually because not only does it deal with proportionalities It also deals with the difference between mass and weight, which is pretty important Remember mass stays the same everywhere in the universe, but weight can change depending on the gravitational field you're in So this is actually kind of an extra bit to this question, which is good if you're reviewing unit B in physics 20 So let's start with a what's the mass of the box on the other planet? Well, what do we have given? We've got the weight of the box and you might remember the weight is really just the force of gravity acting on an object Okay, so we have force of gravity and we're looking for mass We've got a really simple equation that ties together force and mass. It's just Newton's second law and I've written the acceleration in this case is the acceleration due to gravity on earth Because we're talking about the weight on earth of the box So if I want to rearrange that mass is the force of gravity Divided by the acceleration due to gravity 500 Newtons divided by 9.81 meters per second squared So we can pull out our calculator see what we get there I'm expecting My answer to be in units of kilograms. So it looks like we're going to get about 51.0 kilograms That's the mass of the box Like we were saying earlier. It doesn't matter if that box is on earth or in some other weird planet Or in the deepest reaches of outer space its mass stays the same Now the weight will change because weight depends on what planet you're on how strong gravitational field is So to find the weight we can do proportionalities again Let's look at what we have for information for the second part of the problem. We still have force of gravity We also have mass and we've got the fact that it's five times larger and we have radius or the separation between the two objects and We have that that's half as large so the words five times larger and half as larger indicating to me This is a proportionality problem When you're solving a proportionality problem You still need a formula to work from and based on the information given here I know that we're going to have to use Newton's universal law of gravitation Because we've got masses the mass of the box and the mass of the planet and we've got a separation We're looking for a force of gravity When I'm doing a proportionality problem. Here's all I have to do I'm just going to take that equal side. I'm going to replace it with the Greek symbol alpha, which means is proportional to I'm looking for the force of gravity and how that changes, so I'll leave that as an unknown and Whenever we get a variable that doesn't change. I substitute that into the equation as a one Don't actually write that the value of the universal gravitational constant is 6.67 times 10 to the negative 27 I'm actually just going to put in a one Same thing for mass one. I'm going to assume mass one is maybe the mass of the box. It doesn't change Mass two it says has gotten five times larger, so you know what I'm going to do I'm going to put a five in for the mass two five times larger That's what I'm going to substitute in And for my radius this has gotten half as large so in place of the radius I'm going to put in one half You could have also thought of that as two times smaller It's another way that could have been written up here instead of half as large It was two times smaller we'd still put in one half and please make sure you're squaring that value of r squared Just like the formula tells us to do So now we can go through and we can actually solve this in the numerator. We have five should put a proportionality symbol in there five and One half squared is one quarter, so that's 20 Now What does it mean that? The force of gravity is proportional to 20 and why are we putting those proportionality signs in what does the difference? Why do that? Well, I do that so that reminds my kids at this last step that the force of the gravity Acting on this box is not 20 Newtons. Okay. It's not equal to 20 Newtons. It's proportional to 20 Which means that it's 20 times larger Then it was to begin with So if this answer would have come out to 1 over 20, it would mean it's 20 times smaller 20 times larger than our original force of gravity So now when I actually go and calculate the force of gravity, I'll take the original one, which is 500 Newtons And I'm gonna multiply it by 20. This has gotten 20 times bigger So that's going to be 10,000 Newtons or 1 0 0 Times 10 to the 4 Newtons as our new force of gravity So the weight of the block or the box on this other planet is 1 Times 10 to the power of 4 Newtons and we worked that out with proportionality So it wasn't too bad to do we just had to make sure we're using the proportionality sign instead of the equal sign That helped us remind ourselves at the end that this wasn't actually our answer We had one more step to go and I just put in a 1 for any variable that doesn't change and the variables that do change I write in how much they change by If you want to see some more proportionality problems check out my website at ldindustries.ca