**Concept:** Intro to Momentum

Hey guys. So, in this video I'm going to introduce you to a new concept in physics called momentum. Now, I'm sure you've heard the word momentum in everyday language you may even have used it, it's often associated with sports terminology. So, I'm going to show you the physics definition and kind of relate to the everyday definition as well, let's check it out. So, at the simplest level momentum is a physical quantity that combines an object's mass and an object's speed. Now, momentum is given by the letter p, a lowercase p, uppercase P is reserved for power, momentum is a lowercase p and it's a combination of mass and velocity, that's actually just a multiplication of the two, it's mass times velocity, momentum doesn't have its own units. So, it's going to, we're going to look at the equation for momentum to the term of the units. So, it's mass, which is in kilograms times velocity, which is meters per second. So, if you ever forget the units you can just look at the equation, okay? So, momentum is mass times velocity, momentum is a vector and velocity is a vector as well, we'll talk about that a little bit more later. So, momentum is really important in collisions as we'll see throughout this chapter, and the idea that when objects collide what's going to matter is not their mass or their speeds but a combination of those. So, for example, if a truck moving at a very slow speed hits you, it's not as bad as a truck moving at a very fast speed but a car who's much lighter, if the car is moving really, really fast it's actually going to hurt more than a truck, that's moving really, really slow, so the idea that individually these things don't really matter, they matter as a combination of the two. and that combination that matters is momentum, okay? So, in collisions we don't care about mass or velocity visually, we care about the combination of the two. Now, I mentioned earlier the sports analogy and a lot of people will say something like this team has a lot of momentum and it means that they, typically means that they've been winning a lot of games. So, there's a higher chance that they would keep winning games. So, in physics there's an analogy to this, there's a word that represents this an exaction not momentum, this idea that if you're moving therefore you will continue to move where you have a tendency to keep moving is actually inertia, right? So, the tendency to keep winning, let's say, if you are already winning is inertia or tendency to keep losing if you are already losing, would be motion but the momentum analogy isn't completely wrong. So, one way that I like to think of momentum is how hard would it be to stop something, right? So, if you look at m and V you got a car coming at you and if you have to stop the car, the heavier the car the more momentum therefore the harder it is and you can just intuitively figure this out or imagine this, that it's harder to stop something that's much heavier, also if it's moving faster it also becomes harder to stop it. So, one way to think of it is how hard it is to stop something or how hard is it to get something moving, right? It's harder to move heavy objects and it's also harder to get objects to a faster speed. So, with the team, the sports team analogies you can think, if a team's winning a lot they have momentum. So, it's now presumably harder to beat them because they've been winning a lot of games and they're sort of in the zone, cool? So, hopefully that kind of paints a physics specific picture with the equation but also just sort of an everyday language analogy there for you. So, we're going into two quick examples here, just using that equation. So, I have a 100 kilogram, a 140 football linebacker running at 6 meters per second and he's going to tackle head-on in the air this other guy here. So, two guys of different masses, I'm going to make this one like a little bit bigger, whoops, looks like a baby's. So, this guy has a mass of 140 kilograms and is moving this way with 6 meters per second.

The problem, the example doesn't say that it's moving to the right you just said that they tackle head-on. So, I got to pick that one's going to the right the other ones go to the left. So, I'm just going to arbitrarily say that this one's going to the right therefore the other one, a little bit lighter, so I'm going to draw him a little skinnier, is moving this way with 8 meters per second and the mass here is 110. Now, before I do anything else, let me point this out to you. Remember, velocities are vectors they have sign, they have direction, direction matters, it took opposite directions to have different signs, so right away please don't forget to do this, a lot of people forget that, so right away put the signs so that you are safe. Part A says calculate each person's momentum before the collision. So, momentum is just p equals m, v. So, p here, on the mass here is 140 and the velocity is 6 and if you multiply these two numbers and get 840, I'm going to call this p1 and then p2, this is guy 1, this is guy 2, p2 is m, v as well, but with this guy's information. So, 110 and the velocity is negative 8, this is negative 880. Now, the reason why I got a negative is because he's going to the left, we'll talk about this a little bit more later. Remember, the units are kilograms meters per second, kilograms meters per second, this is part 8, I found both momentums and it says, B, if they become entangled in whose direction do they move. So, you wanna see, if we have a better, a more obvious example here would be sort of a bowling ball moving really fast towards a ping-pong ball also moving really fast, you would expect that if they somehow get stuck together they're going to move in the direction of the bowling ball because the bowling ball is much heavier but as I mentioned earlier it doesn't have to do with how heavy you are, with your mass more specifically, it has to do with your momentum and because the lighter guy has more momentum, if they get stuck they will move in the direction of the lighter, lighter, it's ugly, lighter player, and the reason for that is because he has more momentum, cool? So, he's going to win because there's momentum, that's why in football p equals m, v in, football you want to be as fast as possible but you also want to be as massive as possible, as heavy as possible so that you have the most momentum, the tricky part is that if you're more massive it's harder to be to be really fast. So, how can you be more massive and also faster? Well, you have to be stronger and that's kind of obvious if you think about it, cool? So, let's an example to real quick it says, how fast would you have to throw a 145 grand baseball so that it has the same momentum as a 10 gram sniper rifle bullet traveling at 900 meters per second, so the basic setup for this problem is you want to know how fast you have to throw a baseball. So, I'm going to call the ball object1 and I'm going to call the bullet object2 and I want to know, I know that the mass 1 is 0.145 kilograms, always in kilograms and I want to know what must v1 be, I know the information, I have a lot of information, I have the bullet, I know the mass of the bullet, is 0.010, that's 10 grams and the velocity here is 900, I want to know what is v1 so that the momentum of 1 equals the momentum of the other, so this is where we're going to start, p1 equals p2, and I'm going to expand both side in other words, I'm going to replace the p's with m, v's. So, it's going to be m1v1, m2v2, and if you look carefully you see that you have all the numbers except for your unknown. So, mass 1 is 0.145 v1, mass 2 is 0.010 and the velocity is 900 and you now have to just toss this over here, divided by 0.145 and you get that the velocity 1 is, I have it here, 62 meters per second, and out of curiosity actually these numbers are pretty close to what a sniper rifle actually shoots in the weight of a bullet or the mass of a bullet of a sniper rifle closely and just out of curiosity I went to look this up, this is roughly 140 miles per hour, which no one's ever thrown a baseball that quickly, so this is kind of impossible, not that it matters, that's just an example, but anyway that's it for the intro for momentum, I'm going to mention a few more points here and then we're going to do a few more examples.

**Example:** Intro to Momentum

Alright, so continuing here with momentum, momentum is a vector, I mentioned this earlier and its direction, is the same as the direction of velocity. So, if you remember momentum p equals m, V, p is a vector, v is a vector so the angle for p must come from the angle for V, you can just look at the equation, m is not a vector so it has no direction so the direction for p must come from V. So, theta p is the same as the theta V. Alright, and one more point here, if you have an object that is moving in the negative direction, that's typically the left or down but not necessarily, if an object is moving in the negative direction it will have negative velocity, you know that but it will also have negative momentum. So, negative momentum just means you're moving the negative direction, let's do a quick example here then I got a practice problem for you guys, a 2 kilogram object moves in space with 10 meters per seconds directed at 37 above the horizontal. So, let me draw this and I'm going to draw a bunch of arrows here. So, I'm going to try to be very precise or very neat, 10 meters per second here. So, V equals 10 and this angle here is 37 degrees, then it says, A, let's calculate the object's momentum, momentum is p, p is m, v and this is super straightforward, the mass is 2, the velocity is 10 so the answer is simply 20 kilograms meters per second, that 30-degree angle doesn't really do anything, you're just multiplying the 2, and remember also, if I'm going to draw here, which I will, the momentum is in the same direction of the velocity. So, if the velocity is 10 this way and the momentum is 20 ,the momentum is 20 also this way, just longer, right? So, they have the same direction and it's twice as long in this case because the mass is 2. So, p equals 20.

For Part B it says, calculate the horizontal and vertical components of the object's velocity and momentum, the velocity, if I want the resultant vertical component velocity, this is vx, vy and momentum I want px py, okay? I'm going to do it here in the chart, actually I can decompose v into vx and I can decompose v into vy and I can do the same thing with p, I can make a little triangle, this is just vector decomposition, if you are a little rusty should go back to the earlier videos and px is going to look like this and py, so this is py, we leave some room for the number and px. So, I hope you see how p is just same thing as V, just bigger because the mass is 2, so it's twice as big, cool? And then to calculate, this is pretty straightforward the x remember, is v cosine of theta, 10 cosine of 37, that gives you roughly an 8, vy is v sine of theta, 10 sine of 37, which gives you a 6. So let me put these numbers here, vx is 8, vy is 6. Now, when you calculate, that's that, when you calculate px, there's two ways you can do this. Remember, p is m, v right here, p is m, v. So, px is m, v x. Alright, the mass has no direction so there's no mx, it's just m, but you could do it this way or, I'm going to put an or here, you could also have done this, if vx is v cosine of theta then it should make sense that px is p cosine of theta, p cosine of theta. So, you can decompose px itself or you can think of px as m, v x, cool? Either one of these are equivalent, in fact, I could just kind of rewrite some of the stuff to show you how I can go from here to here and they're equivalent forms, it doesn't matter. So, I'm going to use this version here because it's a little bit simpler, because already got all the numbers I don't have to use cosine anymore, the mass is 2, m, v x right there v x is 8. So, this is 16m and then for py, I'm going to use m, v y and 2 times 6, is 12, so this is 16 and 12, I just want to quickly point out, this is 10, 20 that's double, this is 8 and 16, that double, this is 6 and 12, that's double, the reason why it's double is because the mass is 2, cool? So, that's it, those are the different ways that you can calculate px and py, in this example, I could have done it using this or this, in some cases depending what numbers you have one may work and then the other one may be won't work, okay? So, maybe only one of the two will work, that's it, I got a practice problem down here, let's give a shot, hopefully you get it.

**Problem:** The horizontal and vertical components of a 3-kg object in space are 54 kg m/s and 72 kg m/s, respectively. Calculate the magnitude and direction of the object’s momentum.

EXTRA: What is the object’s speed?

3mTwo bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:

A. 1:1

B. 3:1

C. 1:3

D. 1:9

E. 9:1

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An ice skater whose mass is 50 kg moves with a constant momentum of (400, 0, 300) kg·m/s. During this period of constant momentum, she passes the location (0, 0, 3) m. What was her location at a time 3 s earlier?

1. (−8, 0, −5) m

2. (−24, 0, −15) m

3. (−10, 3, −7) m

4. (8, 0, 5) m

5. (10, 3, 7) m

6. (−20, 0, −14) m

7. (24, 0, 15) m

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A planet with a mass of 1 × 10^{23} kg travels around a star in a nearly circular obrbit in the xy plane as shown in the diagram. Its speed is constant at 15000 m/s. Which arrow best describes the direction of Δ* P* in going from B to C?

1. g .

2. f

3. c

4. e

5. b

6. d

7. h

8. a

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You pull a block of mass m across across a frictionless table with a constant force. You also pull with an equal constant force a block of larger mass M. The blocks are initially at rest. If you pull the blocks through the same distance, which block has the greater kinetic energy, and which block has the greater momentum, respectively?

1. Same kinetic energy, same momentum

2. M, same momentum

3. M, M

4. Same kinetic energy, m

5. M, m

6. Same kinetic energy, M

7. m, m

8. m, same momentum

9. m, M

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You drop an egg from rest with no air resistance. As it falls:

A. Only its momentum is conserved,

B. Only its kinetic energy is conserved.

C. Both its momentum and its mechanical energy are conserved.

D. Its mechanical energy is conserved, but its momentum is not conserved.

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