Now we're going to illustrate the laws of conservation of momentum with a watermelon. Why do we drop watermelons from Rice Stadium? Not because it's easy, because it's hard. That was fun. Now we'll talk about the physics and the momentum of the watermelon drop. That's weird. Wait a minute. There are no seeds in this watermelon and I know they can make them grow without seeds, they make them sterile somehow, but this one has dents where the seeds used to be. So there's where the seeds were, but there's no seeds. I just smashed it opened myself, it was closed a minute ago. So how did they get the seeds out? Maybe a chemical that I made. I don't know. I'm going to not think about that, about what chemicals are doing to my body right now, because I swear I opened the watermelon myself when I dropped. Anyway, let's not worry about it. There's no seed somehow. So let's look at our watermelon drop and let's see. So we had it coming down and it fell from on high, like that, smashed into the ground. Let's set up a coordinate system here. So we're going to have plus x that way, plus z that way. So y must be into the board like that. There's our coordinate system. We know what happened, it came down and it smashed and made a mess on the ground. What does that have to do with momentum? Well, let's see. So first let's think about the x-y momentum. Let's look down. So we're going to look down this way so we could write x, y like this. So now here's x and there's y. What do we see if we watch this thing going down? When you looked down, you saw the footage of the thing going down. It's a watermelon and it's falling, and it has no velocity in the x, and it has no velocity in the y. Therefore, it has no momentum in the x. P_x equals 0, P_y equals 0. That's the initial values, P_xi, Px_y equals 0. Then hit the ground and it's smashed. Suddenly stuff goes everywhere, there's this explosion. We'll showing it to you now, and stuff flew around, chunks flew off in all directions like that. Boom on the ground. So clearly, pieces of the watermelon have picked up momentum in x and y. But to conserve momentum, it has to remain 0. The vector sum of all the momentum vectors has to remain 0, because we have to conserve momentum in x and we have to conserve momentum in y. This is why when it explodes, it makes a perfectly round little circle. If you look at the edges of this, we'll show it to you again, it's a perfect circle. As you watch the things fly away, you can see big chunks are always flying away in opposite directions. I found one class where the professor actually made them analyze the video, and estimate the masses of the chunks, and make sure it really does come out to be 0. So here, P_x final, it's still 0, because momentum can serve as a vector. P_y final, it's still 0. This is actually related to how they discover new particles at the Large Hadron Collider and other high energy physics experiments. It's they look for missing mass, I'm sorry, they look for missing momentum. So they know how much momentum went in, they watched the big explosion, they detect all the particles that they know about, and it should conserve momentum. If it doesn't, that means there must be particles that either they don't know about or the detector doesn't detect. So this idea is very similar to how they discover things like Higgs on tops and all that stuff. So that's x, y, some momentum information there. What about z? This is where it looks like we violated conservation of momentum, because the thing stopped. We look into z, the watermelon was falling, it was speeding up at a big value of P_z. That value P_z was changing in time actually. So there's a force in the z due to gravity, dP_z/dt, getting bigger, bigger, and bigger. It was very big until it hit the surface of the earth and then splat, and then P_z equals 0. So there's two ways to think about this; One is, it's not an isolated system anymore. So we had an isolated system of the watermelon, but it had an external force applied to it that increased P_z, and then when it hit the ground, it had a big external force the other way that took that P_z, decreased it back to 0. So if you want to think of the watermelon as the isolated system, it wasn't isolated, it had forces applied. You could also do it this way though. You could think of the Earth and the watermelon together. That's not a very accurate view of the Earth. If we bring the Earth in and we say it's the watermelon earth system, we could ask ourselves what's the momentum of the watermelon Earth system? Well, later we'll talk about gravitation and we'll see that the watermelon feels a gravitational force due to the Earth. But according to Newton's third law and according to gravitation, the Earth feels the same force due to the watermelon. If you calculate the watermelon's acceleration at that height, it's about 9.8 meters per second squared. If you calculate the Earth's acceleration, it's about 9.8 times 10 to the minus 4 meters per second squared. The Earth is so massive, you don't really notice the Earth accelerating towards the watermelon, but it does. So as they accelerate towards each other, the total momentum is 0. This has the momentum growing this way, this has a momentum going this way, they add as vectors and the momentum is 0. Then, they smash into each other, they both stop accelerating, their velocities go to 0, and the final momentum is also 0. So either way you think about it, you can justify this in x, y, and z in terms of momentum.
