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A 60 kg electrician is shot from large spring cannon. The force constant; k, of the spring is 1100 N/m_ The clown is put inside the cannon compressing the spring wi...

Question

A 60 kg electrician is shot from large spring cannon. The force constant; k, of the spring is 1100 N/m_ The clown is put inside the cannon compressing the spring with a force of 4400 N: The inside of the cannon generates constant 40 N frictional force during the 4.0 m that he moves in the barrel: The end of the barrel is 2.5 m above the clown's initial rest position:(a) Draw a free body diagram showing all the forces on the clown as he moves inside the barrel. Which forces are doing work, a

A 60 kg electrician is shot from large spring cannon. The force constant; k, of the spring is 1100 N/m_ The clown is put inside the cannon compressing the spring with a force of 4400 N: The inside of the cannon generates constant 40 N frictional force during the 4.0 m that he moves in the barrel: The end of the barrel is 2.5 m above the clown's initial rest position: (a) Draw a free body diagram showing all the forces on the clown as he moves inside the barrel. Which forces are doing work, and determine if the work positive or negative? (b) At what speed will the clown emerge from the end of the barrel?



Answers

The Great Sandini is a 60-kg circus performer who is shot from a cannon (actually a spring gun). You don't find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1100 N/m that he will compress with a force of 4400 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 40 N during the 4.0 m he moves in the barrel. At what speed will he emerge from the end of the barrel, 2.5 m above his initial rest position?

The situation. We're considering a massive 70 kilograms that's launched from a cannon that has an elevation of Fada 40 degrees above the horizontal. That cannon uses an elastic band to fire the stunt performer, and the band is stretched from its strength like unstained length by an amount ex of three meters. The performer flies free of the band, but the height that he reaches above the floor is the same as the height of the net into which he is shot. Okay, so he takes 2.14 seconds to travel the horizontal distance of 26.8 meters between this point and the net. So his time of travel t is 2.14 seconds in his horizontal distance. That he travels is 26.8 meters. Okay. And I call that l. So first we're gonna set up the conservation of energy equation to the potential energy initially is gonna be equal to the final amount of energy. So we have Initially, all we have is potential energy in the screen, the elastic band, And in the end, we have potential energy, uh, from gravity, right, cause he's some final height above the floor from his from the net that catches him, plus the kinetic energy from the movement. Okay, so this is the amount of energy that he has right before he hits the net. So we can replace thes by our expressions. And we find that the potential energy of the spring, of course, is just 1/2 K x squared where X are out. Where Kay is what we're trying to solve for the potential energy due to gravity is mess times, gravity times the height the net is above the ground. Magnetic energy is 1/2 in times the final velocity squared. Okay, so there are some things we know because we don't know, okay. And we don't know h or v a priori, but we do have the information to find h and be so using our Trigon metric identity that says the sine of the angle theta is equal to, uh, opposite over high pot news. We find that, uh, h the height above the floor is equal to x science data. Since X is the high pot news and H would be the opposite value. So now we have an expression for H. We also want to find the final velocity. Well, they've lost being. The extraction V of X is equal to the the total velocity times the coastline of the angle data or, in other words, we have the which is what we want to find is equal to ah V of X, divided by co sign of data. What's the velocity in the extraction? Well, we know the distance it travels and we know the time it takes to travel that distance. And some philosophy is just distance divided by time with lasting the ex direction is l divided by T. This is still has this co signed it on the bottom. So now we have an expression for V and we have an expression for H so we can go ahead and solve for K. We'll do this on this page. Over here, we find that kay here is equal to mess times velocity squared where again, velocity is equal to elk over tea co signed data. So we'll just go ahead and replace these expressions minus two times mass times, gravity times the height. But we said that the height is equal to X sign data, then this is all divided by X Square. Plugging those values into this expression, we find the value for the supreme constant K equal to 2.37 Tanks tend to the third the unit. You're Newtons per meter, Kalmbach said. It is the solution to our question.

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.

Mm. In this problem, we have to calculate the effective supreme constant of the firing mechanism. What? The supreme constant is a care In order to calculate the supreme constant, we need to apply the law of conservation of energy. So we can white here. One divided by two. Okay, square. This is the total energy, uh, which you the system has initially as equals to the total final energy that is equals to anyone by two. Um, we're not square. This is the kinetic energy of the performer at the point of injection, plus the gravitational potential energy, which is equals two mg h here. This X is the extension in the spring. M is the mass of the performer. We noticed the speed of the performer at the point of injection and then the edges, the height, and we can relate to the high to the extension of the spring through this, uh, figure as a this let's say this is our extension in the spring. And then we have the height at this point which is represented by edge. Let this spring, uh, extension has an has an Anglo theater with the horizontal axis, so we can right here, Peter. So from this figure, we can white here h as h equals two x sine of theta and let this equation is an equation. Number one. Similarly, we can white the equation for the horizontal motion of the performer as we're not X. So this is equals two. We're not consign of theater. This will be our equation number one. By definition, we can ride. This winner takes as we know Texas equals two SX divided by t. Uh, so this will be our equation number three. Now using equation number two and equation number three, we can white here an equation for we note as we notice equals two s X divided by t because I know theater now by inserting this value are Disick waiting for this? We not into equation number one we can right here. Equation one is a one divided by two cake square is equals to one divided by two m and to win all which is equals to a six divided by t cosine of theta old square plus mg x sign of theater. Now this equation can be written for the spring constant K as K Z equals two and into Essex. Divide by X t cosine of theta whole square, plus mg sine of theta divide by X. We call it the question number four. Let's put the values into this question, so it will be care as equals two into 70.0 kg square brackets opened here. We can watch the video for S X, which is equal to 26 point 8 m divide by into 3.0 m into the time interval which is equal to 2.14 seconds into because I know 40.0 degree and we have the square on it, plus the second term which is equals to two into mg which is equals to 70.0 kg into 99.80 m per second square. And then here we have a sign of 40.0 degree divided by X which is equal to three point 00 Mito. So from here we can ride the value for this. We're not as we are sorry for. For this care as a case equals two 2.37 multiple laboratories barred three Newtons per meter. So this is a required answer and of the question Thank you

All right. So for the first part, there's no ah friction force acting so we can directly use thie conservation of energy. So let's say this is the initial point, and that's the final point. So from the conservation of energy, we can say the kinetic energy of the initial point. And the prince's challenge of the initial point is equal to the sum off kind of energy at final point, plus the potential of the final point now at the final points since the spring is fully decompressed. So that means there is no potential energy stored. Everything is, ah, kind of the energy and in here since the velocity zero, as the barrel is still so we can ignore the candidate part. So that means we have the initial o. R. We have the potential, and James's half off Kay Xs squared where X is the compression of the spring is equal to 1/2 off M V squared so I can get rid ofthe D Hafs on DH from that, if it's all for the velocity, we get square root off key over M Time's a Let's call this ex not as the full compression. So that's excellent. So using the numbers, we see that he is 400 newtons per meter and is 0.3 kg and ex not is 0.6 meter. So the velocity becomes six. Find 93 meters per second and in partly we have frictional force acting on the Baron now. So what we can do is hear will add the extra, more extra amount of four work done due to friction in this conservation of energy equation and buy the similar argument as before. We can get it off this Ah, Final Four in geology and initial kind of energy. So we'll have this extra time here, which is he worked. And due to friction, where is the frictional force? An ex Norris decompression. And we have a negative sign here. And the reason for that is since the barrel or since the ball is moving on the right, then the frictional force and the friction forces acting opposite to the direction off the ball which is on the left. So we have a negative sign because they're acting on the opposite directions. Now again, we can write the kinetic energy part and then worked on due to friction which is equal to happen this grade. And if you solve for velocity there, we see that the velocity becomes four point at nine meters per second. And in the final part when we need to find the greatest speed we can, we know that the greatest speed will be when the acceleration and the Net force zero. So let's X is that distance where, um, the acceleration with zero. So that means if we have a barrel like thiss on DH Ex not is the total compression. So when the ball is here are the distances X from the hole, then so, ah, it will be the other part here. So X is the amount that is still compressed. So then the distance the ball has moved his ex not minus X. So, um yeah, so then we can figure out X because we know that force are in our construction forces equal toe the spring constant times X or the distance traveled. So using that we can solve for X, which is f over Kay, where f is six new tenants on DH k is 400 newton for mirrors. Using that X is to a 0.15 meter. Now, if you only used the conservation off energy here as well, we see that the network, the Blue Net, will be the change in kinetic energy. So that's half off. Kay Ex, not squared, minus half off key exclaimed. So that's the sari that's changing potential energy. So that's they want off potential energy that has changed, minus off the work. Done dear toa the distance traveled by the ball. So again there's a negative sign because the the work done and sorry, the friction and the direction of the ball is opposite to each other. So that's as we mentioned that this is the distance that the ball has moved. So that means that distance times, the force of friction will give us the network. And there's a negative sign, as we mentioned. So using that we can solve for the V max, because again, ah, this will be half off in V max squared. So from there, if we solve for V, Max will have the max, which is equal to square root off key over M. It's not squared minus X squared minus two times F by M ex, not minus X and then using the numbers we see, that key is 400 Newton per meter and, um is 0.3 kg. Ex nod is 0.0 six Niedere. We put a square minus. Excess square is zero point 015 meter for the square minus two times 650 Newton by 0.3 Kensi, let's move this a little bit that it's moving around here. Whoops. Ah, sorry. That's a failed attempt that's actually continue in the next bed page. So sorry about that. Speeds crunch. There s o. Let me write that down real quick. So it's 400 needn't per meter. Sierra 0.3 kg, 0.6 meters squared minus 0.15 Needier squared. We put everything side as Brackett and then two times six Newton by 0.3 katie 0.0 point 06 minus 0.15 meter. And then that gives us 5.2. Meaning for second. Thank you.


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Ibuprofen has a density of 1.0? Plan' What is the volume (in L} of an ibuprofen tablet that weighs 250 mg?...
5 answers
Which of the following is true about the A and B pairs below?NHzNH H Handand03a A represents pair of resonance structures but B does notb B represents pair of resonance structures but A does notC Both A and B represent pairs of resonance structuresd. Neither A nor B represent pairs of resonance structuresO=N'
Which of the following is true about the A and B pairs below? NHz NH H H and and 0 3 a A represents pair of resonance structures but B does not b B represents pair of resonance structures but A does not C Both A and B represent pairs of resonance structures d. Neither A nor B represent pairs of reso...
5 answers
According to a recent study, of every 100 people in one Americancity, 48 are considered overweight. The population of the city isabout 1.98 million. How many of these people would be consideredoverweight?Select one:A. 95,040 peopleB. 957,813 peopleC. 888,244 peopleD. 950,400 people
According to a recent study, of every 100 people in one American city, 48 are considered overweight. The population of the city is about 1.98 million. How many of these people would be considered overweight? Select one: A. 95,040 people B. 957,813 people C. 888,244 people D. 950,400 people...
5 answers
Use substitution to evaluate the integral J d 2+4 soludon- Sel (Tnen we cbtzinJ3ziz= f (' (unctian In the variable function In the varlable _"Xhare $ Is a constent
Use substitution to evaluate the integral J d 2+4 soludon- Sel (Tnen we cbtzin J3ziz= f ( ' (unctian In the variable function In the varlable _ "Xhare $ Is a constent...
4 answers
Question 4(15 pointsLet Xi; Xz; Xy be i.i.d. Uniform [0; 1] and Y = min{Xi;Xz Xy} . Calculate E[ Xi |Y]:
Question 4 (15 points Let Xi; Xz; Xy be i.i.d. Uniform [0; 1] and Y = min{Xi;Xz Xy} . Calculate E[ Xi |Y]:...

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