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The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A 30 -caliber bullet has mass 0.00720 $\mathrm{kg}$ and a speed of 601 $\mathrm{m} / \mathrm{s}$ relative to the muzzle when fired from a rifle that has mass 2.80 kg. The loosely held rifle recoils at a speed of 1.85 $\mathrm{m} / \mathrm{s}$ relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

$p_{g}=0.866 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ in the direction of the bullet

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{'transcript': "problem. 8.17. This is about the recoil of a rifle being fired. So we're told a bunch of things. The massive This 30 caliber bullet is 7.2 grams. The philosophy that we use with respect to the muzzle of the rifle it's 601 meters per second and until the rifle has a massive 18 kilograms and it moves if you hold it loosely, she wouldn't really want to do. But Okay, uh, booze at a speed of 1.85 meters per second with respect to the ground or the earth, whatever. And now we want to do is find the momentum of the expanding gases from the gunpowder burning. Uh, because this is, you know, going to contribute to the recoil of the rifle. So and we want to find this with respect of it to the earth. So the first thing we need to do is that it's all well and good to know the speed of the bullet with respect to the muzzle. But since everything we're wanting to do is with respect to the ground of the Earth, we are to find what this is with respect to that other, the rifle and the bullet or moving in opposite directions. So we're going to subtract the speed of the rifle from the speed of the bullet. With respect to the muzzle, the bullet is leaving the muzzle in some velocity. But the muzzle is also moving backwards at some velocity and to the customary three significant digits. This works out to be 599 meters per second. Now everything here started out initially with no momentum because your rifle is standing still. The bullet was of the chamber of the rifle. I'm not moving and the expanding gases didn't exist because they were chemical potential energy of the gunpowder that had yet to be set off. So we know that the total moment has to remain zero because it's always sir. And so this is going Thio. Initially, it's zero. And if we write the Momenta down at the moment, the bullet, the bullet leaves the muzzle of the rifle, then that also has to be zero. That we could find what we're looking for here, which is the momentum of the gases. So even the mass of the bullet times how fast the bullet is going. We have the master of the rifle. Times help ask. It's going and recall. This is going to be negative because it's moving backwards. And then we have the momentum of the gases, which is what we're wanting to fight in the first place. So since we know what this is equal to its equal to zero, all we have to do is so this way we get us pretty, pretty basic manipulation. Excuse me. And so putting all of that in this is the negative because you have a negative sign here. And this is positive. 7.2 grams. I'm sorry. 599 meters per second. And now ve Sabara recall isn't going to be negative. So we're going to get a plus sign. Here is the massive rifle. It's you with respect to the earth. And when you put all this together, you find that the momentum of the gases is 0.8 67 Billy Graham meters per second and this is positive. It's in the same direction. The boat, this travel. So some of the momentum of the rifle going backwards comes from balancing out both the bullet and the gases that are moving in the same direction as"}