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Required information NOTE: This is & multi-part question: Once an answer is submitted, You will be unable to return to this part: Consider the given figure_ Giv...

Question

Required information NOTE: This is & multi-part question: Once an answer is submitted, You will be unable to return to this part: Consider the given figure_ Given P: = 540 N. 800 N40970*30o250Determine the x; Y, and components of the 540-N forceThe X component of the 540-N force is The y component of the 540-N force is The Z component of the 540-N force is

Required information NOTE: This is & multi-part question: Once an answer is submitted, You will be unable to return to this part: Consider the given figure_ Given P: = 540 N. 800 N 409 70* 30o 250 Determine the x; Y, and components of the 540-N force The X component of the 540-N force is The y component of the 540-N force is The Z component of the 540-N force is



Answers

The drawing shows a force vector that has a magnitude of
475 newtons. Find the $(\text { a } x, \quad \text { (b) } y, \text { and } \quad(c) z \text { components of the vector. }$

You have, you can also the non forces on their community. Next, one direction e actually did. All of them are in the Newton on gonna draw it on the plane and find their mind to it. Interaction as well. So, first of all, let me draw the X. I exist over there because it's working with Russian negative reason. Why so, basically, for the first two on one is 200 or two in the negative direction of taxis and hundreds of where direction fixes. So this would be the something like this one. And this angle over there and there is 200 hundreds or the the magnitude of this one will be the 100 times off five year route A route 500 100 Nickens, obviously for this one. And this is so obviously at usually the magnitude and direction would be Justin direction. What will be the direct containing horse of one hour upon to Yeah, pain in the arse off one of 12 That will be the angle. And for this one, this will be 304 100 violent reactions Consists. So the Englewood off this one of the authorities I want to leave. You got to them. First off 314 Well, it's artisan degree and went into it would be 500. And you got 300. 400 square, only 500. And now, next word that this is 400 for the X axis and 300 for the negative wagons. So the single agree with 37 degree and the mentally founded, obviously, And for the same like this one. And okay, so this direction and went to the forces.

Probable has a set of sub problems attached to it. So effectively, we're looking at a B and C here on what we got. We are given the X and Y scale components off some unknown forces on. We have to determine the magnitude and the direction Creech force. So we start with number one Oh A as it is and essentially were given the component off 100 mutants, which is positive, Um, negative 100. Newtons has the white component, so we can see that if we draw a crude set of axes, we've got a 100 compared and coming one way and the native 100 component coming down. So the result in force is here? No, to find the magnitude, we just take the X component, square it at that to the square of the white component and square the whole thing for the magnitude of the force surf A. It's 100 squared plus 100 square and then square root. This if you look a bit about what you can see, that this is going to just be 100 multiplied by route to and so that gives is a value but 141 Newton's to the nearest Newton. And then we simply remember, for our magnet ease we're gonna work from for angle gonna work in a circle, taking the angle drawn from the X axis, the horizontal on. We continue rotating around until we get a number. This tells us what quarter and we're going to be working in. So for the answer of this one, we really just after finding the angle, attention to the angle is gonna be equal to the vertical over. The horizontal tangent is opposite over adjacent in a triangle, so f y over f x. And if we put these values into a calculator, we see that we determine the angle to be 45 degrees. Course we can reason this out as well. They're both forces are equal. Then we're looking and I saw Seles Triangle Triangle with an angle of 45 degrees. Course, this isn't the full answer because we have to work as they were gone from the positive angle direction. Working from X is positive. And so, following this circle, we can see that we've already got 90 degrees here, 90 degrees here on 90 degrees here It is actually 45 plus three times, 93 times 19 being 270 to the correct angle is 270 added on to 45 which is 315 degrees. Okay, so we're gonna do a very similar idea, but we're going to work on the others. Okay? So car team don't be similar. Sort of idea. We've got the to force components. One of 300 mutants, I minus 400 millions. So a different challenge here. And so once again, without crude access diagram, we can see that we've got three hundreds of the left, 400 down. So this is roughly our force on a diagram. Now, some of you may sport that this is actually a Pythagorean triple in disguise. So would do the algebra. Once again. Square root of f x squared plus f y squared. We'll give the magnitude of our force 300 school 300 squared minus 300 squared is 900 and 400 squared or minus 400. Square is 1600 or 1600. Add those together for I SE 900. It's obviously 9000 on a but 160000 for 160,000 anyway, at all those together you're gonna get 250,000 which is square root to 500. So the magnitude of the force is 500. Trust me, just pop it into a calculator and you see that this is pretty accurate. It's in fact, accurate to 100%. There are no decimal places. Once again, I said Pythagorean triple Anyway, we'll move on to the angle. So this is the anger we're looking at here, Onda. We'll just work out a tangent being once again equal to F y over FX. Taking the inverse tangent, we find that the value ease 53 degrees. Once again, this isn't the true angle, as we have to add on the 180 degrees that we took by moving throughout quadrants. So once again, not right on the correct angle that we're after is 233 degrees, cause with angles, it does sort of depend away. It's starting from, so you can see how you might get different angles. The one that book wants is 233 so that it's expressed correctly in terms of its quarter. And for the last one part C. Okay, so once again, we're given the components. Its components are negative. 400 mutant in the X direction, but a positive 300 mutants in the Y direction. So quadrant diagram. Once again, we move to the left, we move up. So this is the rough direction off our force when the angle is measured this way. Okay, so let's make a start with the figures. Once again, we're looking actually the same figures as last time. Negative 400 squares on Dad's to 300 squared. So using the same technique FX squared plus f y squared and taking the square of this pop it into your calculator and you can be reasonably sure the magnitude of your force is equity 500 mittens. Okay. And what about that angle? Well, same rules. Is before attendant is gonna equal if what ever? FX. We've already done this one. We've seen an angle of 53 degrees on that angle is here 53. And so you know, to find the true angle for the problem, we need to take 180 degrees and subtract off 53 to give you an angle off. 143 143 Deaths help facing nonsense 100 on 27 degrees ALS sorts of different romances there because if you put these figures into a calculator with the correct negatives, the calculator will give you appropriate angles. However, the calculated works with negative angles if they are in the bottom two quadrants, and you have to remember to correct these to become some sort of angle working from 360 backwards use this method. This works, but a bit of common sense really helps just in order to work.

Again the component off random forces and you to draw it on the excesses on the, uh, the 100 the manager. And the direction is well, so every horse over there is in the Newton year because they're in this also hand up, Let's say the X axes. Did you try it? Better of you. So this is the X axis y axis. Actually, this is the X axis, and this is why I exist. So 100 in the X direction This is X and Y over there. So let's say this is X or there is 100. So 100 would be this watch and a 100 so there will be a force in this direction, which is you do with the important 45 degree with the X or Y negative off axis and when YouTube will be just hundreds 400 Scott, that would be 100 due to. On second force were 304 100. This will be 300 in the negative and 400 in the in the hour. So this will be obviously the horse which have yeah, and this angle over there will be heard 37 degrees. When you calculate on the magnitude of this force that only 500 Newton over there. Obviously he didn't. When is 403 100? That would do in this direction on this angle over there, that this angle over there, this will be 37 degree and you calculate, and then it should obviously only 500 million. Okay, this is a component of his forces on the coordinated accesses.

All right, I've stopped drawing the diagrams because it's easier just to look at the diagram in the book. Um, diagrams don't seem to be helping. Ah, whole lot. Now, I noticed that the Force F, which is 300 news. It has a component in the Y direction, which is just f co signed 30. So f in the Y direction is just of course, signed. 30 300. Code sign 30 is to 59.8. Now, the remainder of it is in the direction. Doesn't really give us a point. Um, but let me draw this diagram at least a little bit. Got this, Which has point a here. I don't see a point B. So I'm gonna call this point b in the diagram, because kind of like this, like this. There's where the X axis is Z axis and, ah, this is the Y axis here. Okay, I'm gonna call this be and so f in the b a direction. It's going to be the square root of 300 squared minus 2 59.8 squared. So has put that into a calculator. I guess I could have done find good night. Oh, well, but it is just 100 50. That would have been f sign. 30. Silly me. All right, but that is 30 degrees to the Z axis, and so f sub ax is going to be f. So be a times the sign of 30 degrees. It's in the negative direction, and f sub y was in the positive direction. But F sub acts would be in the negative direction, so it's just half of that again. So that would be negative. 75 Newtons, and so those are my answers.


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