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Find vector F = D Eby following the steps the Tactics Box above Make corain araw Ewith tro corroct orientation:Label Vectors D Fitst vectorLength: Angle: Start poin...

Question

Find vector F = D Eby following the steps the Tactics Box above Make corain araw Ewith tro corroct orientation:Label Vectors D Fitst vectorLength: Angle: Start pointEnd point

Find vector F = D Eby following the steps the Tactics Box above Make corain araw Ewith tro corroct orientation: Label Vectors D Fitst vector Length: Angle: Start point End point



Answers

For the vectors given in the following figure, use a graphical method to find the following resultants: (a) $$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$$ , (b) $$\overrightarrow{\mathbf{C}}+\overrightarrow{\mathbf{B}}$$ , (c) $$\overrightarrow{\mathbf{D}}+\overrightarrow{\mathbf{F}}$$ , (d) $$\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}$$ , (e) $$\overrightarrow{\mathbf{D}}-\overrightarrow{\mathbf{F}}$$ , (f) $$\overrightarrow{\mathbf{A}}+2 \overrightarrow{\mathbf{F}}$$ , (g) $$\overrightarrow{\mathbf{C}}-2 \overrightarrow{\mathbf{D}}+3 \overrightarrow{\mathbf{F}}$$ ; and (h) $$\overrightarrow{\mathbf{A}}-4 \overrightarrow{\mathbf{D}}+2 \overrightarrow{\mathbf{F}}$$.

All right, now, to try to draw this one since seems pretty difficult to draw. So we got a point here. That is five and seven, and we call it Point B. So I'm going to draw a vector. Teoh here and it is groups seven feet, five feet. Call that point B. Now I'm also going to draw the other vector two point A and, um, that one has a projection into the X Y plane of 30 degrees, and then there's 70 here, and this is 10 feet. Okay, so I'm gonna call this u sub A and I'm gonna call this you. So be so. You sub a is going to be. Well, let's get the X direction component that's going to be 10 feet times the co sign of 70. That's gonna take it into the X Y plane, and then it's gonna be times the sign of 30 and that's gonna be in the eye direction. It's also going to be negative because it's clearly in the negative I direction plus 10 who signed 70 co sign 30 not to be in the J direction, and it isn't the positive Jay direction. And then in the K direction we've got 10. Sign 70. So that's that's you a, uh, graduate my k here. So it's negative. X positive. Why? Positive Z. Okay, you Beav actor is going to be well, it's going five in the positive extra direction and it is going seven in the negative y direction. So if I want this vector here, all I have to do is you b minus you a and I'm gonna call that you a b So subtracting the i components, it's going to be five plus 10 co sign 70 sign 30. It's in the eye direction. All right, um, subtracting the the B components. I mean, the Jada Direction components is gonna be negative. Seven minus 10. Who signed 70? Who's 30 in the J direction, and then the K direction is just going to be plus negative 10. Signed. 70 que Direction B minus A. Right. Okay, so I'm trying to figure out the magnitude of the oh, the force as a Cartesian factor and it's direction angles. Okay, well, the force, it is just gonna be the force times you a B vector over u A B. This is the u. A. B vector, but U A B is going to be the square root of five plus 10 creekside 70 Sign 30 squared plus negative seven minus 10. Who signed 70 Could assign 30 squared. Plus my goodness. Negative. 10 sign 70 squared. All right, so what I'm gonna do is I'm gonna put that into a calculator. This is more complicated than I had hoped for. Root of five plus 10. Who signed seven b. No sign, no sign. 30 squared us. Negative. Seven minus 10. Co sign seven b Who signed 30 squared plus negative 10 Sign seven B where that gives me 15.3 and this is in feet. That makes sense. All right. So for the x component, I need to take five plus 10. Who signed 70. Signed 30. Put him to my calculator. And then I need to divide that by U A. B, which is 15.3. And then I also have to multiply that by the force. Are we given the magnitude of the force? Oh, yes, we are. It's like I didn't draw that on the diagram, but it's £135. So the force in the X direction is the is the force times you a B X over u A b where this his u a b X. So I put that into a calculator and I get 59 0.4 f y and fz using the same concept is me are negative 88.1. And by the way, these are pounds and negative 83.2 pounds. Now, does that make sense that why in zeer Negative but X is positive? Yes, it does make sense based on the drawing. So again, what am I trying to figure out? The Force f. Okay, so the force is the square root of f X squared, plus of why squared less F Z squared? Where Route. Wait a minute. Already. Know the force express the forces a Cartesian vector. Okay, my bed f equals 59.4 I minus 88.1 J minus 83.2 k And let's just make sure that that's correct by looking in the book 59.4 I minus 88.2 J minus 83.2 k That's correct. Um, I didn't think I actually rounded at all here. I don't think I did. So the book says 88.2. But I disagree. 88.1. Um okay. And determine its coordinate direction Angles. Well, now, this is just what we had done in the last section after 135. Okay, 60 3.9 degrees. And if I put in negative, 88.1 get beat as 131 degrees and gamma, I just have to put in the numerator Negative 83.2, 28 degrees, so

When this question women given the magnitude of victory f and dangle t tell a trip makes with the positive X axis. So the X component off will big toe have cost time, which will be quarter 30 cause 285 degrees. It will be quarter to 7.76 Only the white component will be quarto have signed it. Uh, this will be called 30 Sign 285 takes days, which will be quarto minus 28.98 So F in component form can drink tenderness effects Comma five, which is a quarto 7.76 comma minus 20.98 and F in vector component form can direct in a 7.76 I minus 28.9 it Jay.

Okay, So if we have vector X. Prospector P equals let us so let's fight back to app, lets find X. Okay, So let's see this is vector P. Right? And this is back to F. Okay, So which vector ad dr B equals vector as so it's very obvious, X equals vector A. Right.

In a sector science. We have five editors, ABC indeed that are shown here on stream. And we have to find, um, several operations between the vectors And in order to do that, first of all, I'm gonna find the component of the factors of each one of the factors. Ah, considering that the coordinate system a search that the why exes is pointing out boards in the X axis is pointing to the right. So let's right. Ah, each vector in its component form. So we have a that is equal to the magnitude of a that's 10 times the cool side of 30 in the, uh, extraction, plus 10 times a sign of 30 in the Y direction. So, Jay, I is a detector in the extraction Jay's unit vector in the Y direction. So, uh, carry out the multiplication. We have a A is, uh, 8.66 times. I was five j. The is five times the coal sign of 53. I lost five times the sign of 53 J, which is able to three I plus 3.99 j. And we have see noticed that C is pointing in the negative direction in the Y axis, but in the positive direction in the axe axis. So this is equal to five. Ah, actually, the it's a fine. It's the magnitude of the sea. Vetter is 12. I hadn't written it, but it's well, so we have that C is able to the magnitude times, of course, sign of 60 in the X direction, minus 12 times a sign of 60 in the Y direction because it's pointing downwards. So this is equal to six I minus 10.39 g. Then we have to find Victor de. He has, ah, magnitude of 20 and it's pointing in the negative extraction and in the positive Y direction. So this is minus 20 times, of course, out of the angle, which is 37 I plus 28 times a sign on 37 Jay. So this is equal to minus 15.97 I plus 12.4 j and F finally has also make it 20 and it's pointing that I've negative direction both in the X and Y axes. So uh, minus 20 cool side of 30 degrees I minus 20 sign of 30 j. So This is people to minus 17 points. 32. Why minus 10 j Okay, so now we have all these vectors and we can start solving each question in question. A. We have to calculate a plus B. So what we need to do is Teoh some A and B component by component. So in the X important, it's 8.66 plus three. That's 11.66 I less, uh, in the y component. We have five and 3.99 so it's 8.99 j. This is the answer to question a question. Be we have to calculate C plus B Um, so it's six plus three in the Y direction in the maternity extract and minus 10.39 plus 3.99 in the wide reckoned. So this is minus 6.4 J In questions, see, we have to calculate D plus F. So it's minus 15 point any seven minus 17.32 in the extraction. That's minus 33 point dining going 29 hi, then have 12.4 minus 10. That's minus 2.4 in the y direction, then question d asked this copper lead a minus bi. So in the, uh, let me just write it a little better. So in the extraction, we have 8.66 minus three. That's five point, uh, 66 I plus, in the wider actions, we have five minus 2.99. That's 1.1 J in question E. We have demon is F, which is equal true in the extraction, it's minus 15 97 plus 17.32. And that is, uh, one point 35 I. And in the Y direction, we have 12.4 miners Manus tan or plus 10 which is 22.4 j. Uh, then we have I'm gonna just start solving right here on the side. So for the if the question we have to calculate see, minus two d plus three f So this is in the X direction. It's six plus two times, uh, 15.97 minus three times 17.32. So that is equal to, um I'm sorry. Uh, this is actually the answers. A question g Not to question after. I'm gonna ah, do question after right after this. So this is equal to minus 14.0, to in the act direction and in the Y direction we have minus 10 1 39 minus two times 12 went, 05 minus three times 10. And that is minus 64 0.47 j. Yeah, in I go back to quit enough that I had skipped. It's a my A plus two f So this is in the extraction. It's 8.66 minus two times 17.32. So this is equal to minus 20 5.98 I, and in the Y direction, we have five minus, uh, 20. So it's minus 15 j. And now why don't leave for question H. We have a plus minus for D plus two f. So we have, um, in the extraction. We have 18 66 ah, plus four times 15.97 minus two times 17.32. And that is equal to 30 7.9 I. And then in the Y direction. We have five minus 4.12. I'm sorry. My minus four times 12 went, 04 plus ah, minus 20 which is able to minus 63 0.16 g. This concludes the exercise


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