11. Momentum & Impulse

Intro to Momentum

# Momentum in 2D

Patrick Ford

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Hey guys, let's take a look at this problem here. So I have a two kg object like this and I'm given what its velocity is, Its velocity is sure I'm told is 10 m per second and it's some angle above the horizontal, 37 degrees. So let's take a look at the problem here. And the first part just calculate the objects momentum. Remember that's just P. And we have this equation for P. P uses equal to Mv notice that we don't have to do any vector decomposition, there's no sign and co signs just yet. All we have to do is multiply the mass times the velocity and the momentum will point in the same direction. So our p vector is just gonna be the massive two times the velocity which we have and that's just 10. So momentum vector is just 20 kg meters per second. And that's the answer. So one we can kind of understand this, is that the velocity vector is 10 this way. And basically, because the mask is to the momentum vector is going to be exactly double in the same exact direction here. So this pea is just gonna be 20. If the mass were three, the momentum would be three times as big and so on and so forth. So we have this momentum vector, I'm just gonna call this is 20 for now. That's the answer. So let's take a look at part B. Now, part B. Now we actually want to figure out the components, the horizontal components and vertical components of the velocity and the momentum. So basically that's just V. X. And V. Y. And then we want to figure out PX and py so let's go ahead and do that. Well DX and Dy are very straightforward, right? We have the magnitude the 10 m per second and the angle. So we've done this a million times before. The extra six is gonna be 10 times the Kassian of hoops, 10 times the coastline of 37. And you've got eight, it's eight m per second. So this is V. X. Here, the Sequels Eights and V. Y. Is just gonna be 10 times the sine of 37 you get six. So that's the component there. So you basically just have a um V. Y equals six. So this is basically a 68, 10 triangle. Right? What about PX and py? Well there's actually two ways you can kind of understand and make sense where PX and Py are. Well, one thing we can do is we can say, well if P in two dimensions equals M times V in two dimensions. And if we want P. X we're just gonna multiply mass times V. X. P Y. Is just gonna be M times V. Y. Right? So if P equals M V P X equals M. V. X and so on and so forth. Another way you can kind of think about this is that p is just equal to if this is a vector then the X component is gonna be the magnitude times the cosine of the angle. That's 37 degrees same thing's gonna happen with the y axis. So p. Y. Is just gonna be p times the sine of 37. We can use the same angle here because again these these vectors are gonna point exactly along the same direction. So that means that they're thetas are going to be the same. There's two different ways you can think about and you're gonna get the right answer for both of them. Let's check this out. So we know the mass is just too and the V. X. That we just calculated over here is just eight. So if you work this out, what you're gonna get is 16, you're gonna get 16 kg meters per second. So basically what happens is that the X component of this momentum here, this P. X. That we just calculated is 16. Notice how it's just twice whatever this was the same way that this was twice whatever the velocity was. So another way you can think about this is we could just use P. X equals 20 times the cosine of 37. And you're gonna also get 16 here, let me go ahead and just scoot this down a little bit. So notice how you just get the same answer for both calculations here, you'll get 16 either way. So that's what PXE PXE is you do the same exact thing for py so this is gonna be two times the six and you'll get the 12, that's kilogram meters per second. Or you can just do um You could just do P. Y. is equal to 20 times the sine of 37 and you'll get 12 as well either way you get the right answer. Alright so those are the components eight and six and then we have PX and PY. So basically just finish off this little triangle here, we've got the Y. Component of my momentum and it should be twice what the velocity is, what P. X. Is 12. So notice how this is 10, this is 20 this is eight and this is 16 and then this is six and 12. Basically everything has scaled twice in each direction. That's about this one. Guys let me know if you have any questions.

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