Welcome to a new spring problem. So this time you have what you call a spring gun. But this is our spring gun right here and inside of it. Uh, he's a compressed spring, but this distance of compression well extended a little bit. Thiss distance off compressions. Six centimeters if you change that too. No, you know, we can call that, you know, instead of just calling it six centimeters, we call that our distance X if you want to. So x happens to be six centimeters. We changed that two meters as science standard units. So one meter for hundred centimetres and that becomes open their six meters. So what's happening in this problem is that you have a ball inside off this spring gun borrow the spring. Constant happens to be a k Okay. He pulls too. Four hundred home Newton from meter in the spring has a negligible math. So this spring has naked people mars and that that house is in the problem, so it doesn't complicate the problem. The muscle the ball happens to be own zero point zero three zero zero kilograms and it's a horizontal bar. Also, the spring is gonna be released, and when it's released, what happens is it pushes the ball up until the edge of the bar. Oh, so if you look a tte, this would be like a before and after scenario. This is after this is where this this spring starts. This is the point of release. So it's gonna kind of like stretch all the way up until there. So you still have the ball at the end. So it's interesting than that when it's released, takes out the ball, but the barrel itself is six centimeters long. Could the borrowed six centimetres long? So I think we should kind of like indicate that that this barrel, this distance right here happens to be six centimeters and then this is like outside. Okay, this is outside right here. So this is all outside and they the spring there, there's a bow. Maybe I need to help me. I need to open this cause the ball is going outside. So we want a model the Dag Lem, to show this is open because it's allowing the ball to go outside. So pretty much what's happening in this problem is that you have a spring that's pushing a ball outside the spring as the spring constant of four hundred Newton, Amita and in. But if the problem, we want to find out the speed with which the ball leaves the barrel. So what's this velocity here? We're gonna use the law of conservation of energy which say's energy before equals to energy after energy before equals two Energy after the energy before is toward us elastic potential energy. And that happens to be one half k x squared the energy after his stored in terms ofthe the kinetic energy off this ball right here. So this ball develops the type of kinetic energy because it's moving and we want to solve for this velocity. So you can see who divide both sides by I one huff. We divide both sides by one half em to make our life easier. This is just algebra one of Zambia, one ofthe Emma. You can see the one house and one to cancel out and the EMS Iguana Council out. So three squared happens to be okay X squared of him. So the velocity with which the ball these darl uh, his quote of cakes would hold him plug in the numbers. K is our supreme constant right here. It happens to be four hundred Newton a media and then the displacement of distance that this ball moves before it leaves outside or before it leaves, displaying a zero point zero six meters toe plug in that always a good habit to keep track of the units and then divide by the Marcel's bone. The masked ball, as you can recall, is right here. It happens to be zero point zero, three hundred three point zero three kilograms. So we keep track of all the units again. This is a square root plug in the numbers. You notice the final velocity. His sama is six point nine meters per second. So you know, that's the lofty home that the ball huh's once leaving the bar off the image just crosschecking the end point zero six and then divide by zero three accusers. So four hundred Um, you do that again? Oh, yes. So swollen four hundred times this one is going to be squared. This one is quite so with you, don't you? Don't forget that Here. Point zero six, right. Bye. One zero three. They tried again. Second shift More hundred times when zero six times six. No times divided by When you're three. There was a rocket. Yeah, six point nine or concerns six point nine weeks. Well, you know, just to be a little bit more precise who call this six point nine three. So six point ninety death, the velocity of the ball. These the barrow Second part of the problem is that I want to get the speed of the ball if there's a constant resisting force inside the barrel. So this is part B. Um, there is a constant force inside the barrel. So once again, you know, you got that he had to borrow. And then you have this spring. This's the initial position of the ball. It pushes the spring, pushes the ball all the way up. But these are resistance force acting in the opposite direction. So there's a force that resisting in the opposite direction Oh, because it's a resistant force and want to call it f fr. You can call it a half hour. So from the the spring itself has elastic potential energy, which is one half OK, X squared. This force has is working against that. So what done by the resistance forces f R times the distance that the ball hostiles. And so if you put those two energies together, you get one half k x squared minus R Close it times x This one right here This is the home. This is the energy that the, you know, the spring exacts on energy on the ball, equivalent to one half k x squared and then the force exactly opposite energy on the ball, which is equal to have our ex. So this is energy due to the spring and this energy due to the force and that should equal the kinetic energy off the off the ball itself. So one half and V squared and then we can make our life easier by multiplying everything by two. That's where you're going to cancel this one half in that one house. So we end up having n V squared equals two K X squared, minus half art times X. We divide portside by the Mass, which is him on DH. Then at some point, we need to, uh, we end up having V squared equals two K X squared, minus f car time. Stacks of him and the velocity becomes this quote of that which is K X squared minus fr times x over em. You could pull out the ex we have screwed of x okay, minus f r well of him on DH and then we need to plug in. The numbers are going to continue that right here X If you go back, happens to be zero pens or six. This is opens their six meters. Remember, it's X. This would be K X rayed here and forget the jacks and then we have K X K happens to be four hundred Newton meters times X, which is opened zero. Six meters minus the force. Go back. You see that of the you know there's a There's a resisting force, that stopping call form going outside and we need to include that resisting force, which happens to be oh, which happens to be remember, there's a to here, so let's not forget that you know, there's a two right there. The two right there. There's two right there with two right there. So there's a resisting force minus where to times the resisting forces six Newtons. You know, if you can recall this force right here. It's six Newton's so two times six new tenants and then times. So So in that case, what we have to divide by the moss, which happens to be zero point zero three. There's airplanes or three kilograms. When you solve that, you get that the velocity. The speed goes down to four point nine meters per second. So once again, what's happening here is that at the beginning, then have any resisting force those just spring pushing the ball outside. So we used conservation of energy energy before it was too energy. After before energy was one half k exploit. That's from the spring. The after energy was the kinetic energy that Iqbal gains. Remember, all the elastic potential energy from the spring is transformed to the kinetic energy off the off the ball allows us to solve for Visa Good. Happy to keep the variables up until the end, and that's what happening. What's happening right there. Don't forget this square sign. Easy to forget small things like that. And then you get six point nine three and the other part of the problem. Now we have a force that's resisting the motion. So in terms of conservation of energy. This is energy before equals two energy after law of conservation of energy that before energy is reduced by this frictional force, not fictional force. But by resisting force, we check O f our so f our times X that's subtracted from the elastic potential energy. And you make that equal to the the energy after, which is the kinetic energy that bald gains you saw for V's wed and then keep the variables up until the end. It's a good habit. At this point, you're saying I'm pulling out the excess for purposes of algebra, and then I'm left with K X inside on, then minus two f r m solved that you get four point nine meters per second on the next part of the problem. We want to know you know what's gonna happen in a different case. So you still have that we have. The spring was healing s o. I've just magnified it, you know, this is your opens their six meters, and then they're certain assumptions that we're making that I want to know what's the point where the ball has the greatest speed. So I'm going to call that X X Great ex greatest. That's apparent where the ball has the greatest speed, the spring provides ofthe force, which is if he was too. Okay, Times x greatest. So this is the same as Ex Greatest being You called too. Averages Spring Force over the, uh, K, which is the spring constant. And so we have six Newtons, four hundred, a Newton meter that gives us a zero point zero two meters. And what that means is that the distance all the way up until the richest our force, this distance right here is zero point zero two. And so Oh, you know, that's that's the distance moved by the ball s O. So you know, we have to backtrack a little bit. This one right here. This one idea, Uh, this one right here. So the oh x ex Greatest, your eggs Now the greatest His huh is the same as you know that that that hold the distance moved by the ball is given by six Newton's over four hundred on that, that's going to give us what six Newton performed. So let's see. Six. Divide that one hundred that zero point zero one five. This is this. Is there a point? This is zero point zero one five meters. When you run it off, you get zero plans or two meters. So the the actual distance moved by the ball. You know what you call Delta X becomes their point zero six. That's the total distance from right here, right there. Well minus minus zero point zero four. Minuses. Opens or two. Sorry. And that gives us a zero point zero four meters. So that's the distance moved by the ball. Oh, the other part of the problem. The last part of the problem we have to use the that The total work involved in the parks of using Tor a walk is we want to find out what's the but the greatest speed. The they think the greatest speed. You know what? I should I should just call this instead of X. Great. I'm calling it X Greatest because this is the point where we have the greatest speed. Okay, that's the point. Really. Antiquated speed. So we want to compute that were using were still using the law, the love total walk if you want to call it that. So that's the kinetic energy plus home. Any other external walk, the supposed to elastic potential energy or or changing elastic potential energy. So this one we can call it changed in the last potential energy going race that, um right here, zee hold to change elastic potential energy. So changing kinetic energy up until the marks and velocity we have m v squared. Greatest equals two not equals to, but plus, we're using the total work. Um, plus the force. It's going to take the resisting force up until the end, minus up until the greatest position on which is so ex greatest happens to be. And I'm calling it zero point zero two expletives two's open zero to some miners Ex greatest. That's a special location equals to one half. Okay, our X squared minus X greatest squared. So that's just the change in elastic potential energy that happens. So, you know, this is the change in, and this one right here is the change in, uh, walk down by the resistance force changing walk down by the Resistance Force. This is changing the last potential energy. So we multiply everything by two. We call life easier. So this is empty. Greatest spread plus two f x minus X greatest equals two. Okay, X squared minus X. Where greatest. So it can be a land gone long. Problem or goal is to get this one v greatest. So, um, we're gonna have on the next page, we have m v greatest squared. He close to move everything to the other side. Get Kay. Hey, X minus X greatest squared or both of these squared minus two f x. You know, we're taking that number at their X minus her ex greatest again. I'm gold still to solve for we squared greatest So you can see that of the square Greatest is kay X squared minus x great greatest minus to f X minus X greatest all over. I am so this M You know, we're divided on both sides, as you can see. So now we're ready to find the final blast ease or the greatest. It's just gonna be this quote off all of these numbers, so we plug in those numbers and get no. Four hundred New leader times X, which is Oakland zero six. We need a sweat minus. Um, we have a bracket here minus X greatest, which is your point zero to meat is squid men minus two. The force is six Newtons. Then we're going to get a zero point zero six on the silken zero two. That's the change in displacement, all of the mass, which is your point zero three zero kilograms and so final once that happens to be five point two meters per second. So that's the largest speed as the greatest speed, the V greatest toe once again, a long problem involving a spring in a ball. The spring is pushing the ball outside the bar. Oh, so we want to find the velocity when the ball gets to the mouth over the barrel, which happens to be six centimeters. And that's what we got right here. This velocity are using the law of conservation of energy before his sins. After the energy on one side, we have elastic potential energy. On the other side, we have, ah, kinetic energy in the second part, the oven external force coming in. So we have to account for that. The external force he's taking away from the kinetic energy and this is what's happening. This is the kinetic energy, and this is the external force, So it's reducing the kinetic energy. Um um and it's reducing it because it's reducing the elastic potential. So we'Ll make that equal to the kinetic energy we solve for V by reorganizing the problem, keeping our valuables up until the end. The next part of the problem. We have to find the point of which the greatest speed happens. Use hooks, Law Africa. Lt's too of K X and soften Ex Greatest, which gives us Europeans or two meters. We I can get the change in displacement by subtracting it from the largest land and then the final part of the problem. We have to use thie total walk formula where we say, you know, the the total walk down in the whole system is a constant stays same. So you know we have K kinetic energy at the greatest location is sama's. The changing walked down due to the resisting force at the greatest location, which is equal to elastic potential energy with plug in the numbers, we do a lot of manipulations and you can see at this point we saw for the very greatest, which happens to be five point two meters per second so Thank you very much for watching the video Have a wonderful day. If you have any questions, send them my way on. I'Ll be glad to respond to your questions. Okay. Thanks. Bye.