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(II) For the vectors given in Fig. 38, determine $$(a) \vec{\mathbf{A}}-\vec{\mathbf{B}}+\vec{\mathbf{C}},(b) \overline{\mathbf{A}}+\vec{\mathbf{B}}-\vec{\mathbf{C}}, \text { and }(c) \overline{\mathbf{C}}-\vec{\mathbf{A}}-\vec{\mathbf{B}}$$

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a.$53.7 \hat{\mathrm{i}}-32.3 \hat{\mathrm{j}}$b.$24.0 \hat{\mathrm{i}}+73.7 \hat{\mathrm{j}}$c.$-24.0 \hat{\mathrm{i}}-73.7 \hat{\mathrm{j}}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

University of Washington

University of Sheffield

University of Winnipeg

McMaster University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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For the vectors given in Fβ¦

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(II) For the vectors givenβ¦

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(II) For the vectors shownβ¦

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07:01

0:00

(II) Determine the vector β¦

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06:28

16:17

05:02

For the vectors shown in Fβ¦

00:35

Given vectors $\mathbf{u}$β¦

02:50

In Exercises 31-38, find (β¦

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Determine the vector $\oveβ¦

09:07

Compute the $x$ and $y$ coβ¦

04:48

08:07

05:15

For the vectors $\vec{A}, β¦

02:11

01:20

For the vectors in Exercisβ¦

Our question says for the factors given and figure. 38 determined, eh? Vector a minus. Vector B plus C B vector A plus B minus C and C vector C minus a minus vector be okay. So I wrote down what we have given based upon looking at Figure 38. So we're given that the magnitude of Vector A is 44. The magnitude of Vector B is 26.5 and the magnitude of a vector C is 31. The angle A with respect to the X access that plus going in the plus X direction. So that's starting at zero degrees at that On the right side of the ex, access going up is 28 degrees, we're told B it shows that it's 56 degrees, but that's from the minus X axis. So that's actually 180 minus 56 degrees. And that is 21 124 degrees. Okay, and so that state of B and then data see is 270 degrees. And that is because they to see the angle of sea is along the minus y access. Okay, so the question is determined the following and I wrote out what a, B and C, as I previously stated, are In order to do this, we're going to need to determine the ah when he determined a which is made of a of X plus a of why b which is made of B of X plus b a why and see which is made of sea of X plus c of why so we need a vex and of Lybia vax B of lai See ataxia. Why, In order to do do that, we're gonna go ahead and do that calculation here. So an ex is equal to So this is the X component of vector, eh? The magnitude of a multiplied by the co sign of eh co sign because it's in the extraction. So 44 times that co sign of 28. If you play that in, that gives you 38 25 money. Go ahead and all of this so you can keep that separate from our solution that were working here. A y is the magnitude of a times that co sign or I'm sorry, not co sign because it's why it's timesthe site of England Okay, this is 20.66 Okay, now we need to do the same thing for B be of X magnitude of B sometimes co sign because it's in the X Could the angle B So magnitude to be is 26.5 times that co sign of 124 degrees, and that's going to be negative. 14 22. That makes sense because B is pointing in the negative X direction. So the ex complaint of B is negative. 14 0.2 yeah, and now he wanted to determine the Wycombe poet. He said Why? And as before we're in and multiply the magnitude of B timesthe sign this time because it's the white from hone it because the angle it'd be so 26.5 times co sign of 1 24 is going to give us 21.97 Makes sense that it's in a positive. Why direction? Because B is in the positive direction. Okay, and lastly, we need to do this for see so see of X is going to be the magnitude of C multiplied quite a co sign, see, But they had to cease to 70 there's no X component of X or have C, right? It's in the native y direction. So just intuitively we know it's going to be zero plus the co sign of 2 70 a zero so intuitively and mathematically it's zero and then see of why? Well, let's just jump right to the answer. Because this is pretty easy with same logic to get too, because the co sign of negative to 70 is our of 270 degrees is minus one. But we know that all of C is in the Y direction. It's in the negative y direction. So the secret there, the white component has to be minus the magnitude minus 31. Okay, Now, using all of these were we can determine the vectors that were asked to calculate for part A. B and C ran out of room here. So we're gonna go ahead and go to a new page, and we're going to start with part, eh? So cool. Label this Cartier okay. And part A asks us to calculate a vector, eh, Linus? Vector B plus sector c. Well, you can on ly add like components, so we have to add the we have, er you can on ly add and subtract like components. So we need to carry out these actions for the ex components of A B and C and the white components of A, B and C and you're gonna add those together to get your new vector. So you have a minus b pussy when we kick in here, if these are the X components, So your career that action out for the ex components of the vectors Hey, and then you're gonna add that to this being carried out to the white components of the vectors? A minus B plus c. Okay, well, as we already previously calculated the on the on this page Here we go back and look, we have the X. Why components of all of these values. So we have 38 for a X. We have 38.85 minus the ex component of B, which we found to be ah, fort minus 14.82 So this is minus minus 14.82 and the ex component of sea was zero. So we don't have to put anything there. And this is all the ex component. Okay, make sure it doesn't look like the wind. Yeah, And then we add the white component doing this delight in front of the white component of a was 20.66 minus the d component, the white component of B, which was 21.97 plus the why component of sea, which was minus 31 plus the natives just minus. So we can write that as minus 31. Okay, that's why this. And if you carry the sound, if you go ahead and do those calculations, you will find that this comes out to be 53 0.7. I'm gonna write this in the eye hat direction, which is X direction. It's another to notation for ex direction. And this is Susan. Plus and minus 32.3. This is in the white hat direction are also Jay had direction. Okay, okay. And the reason we report this to three significant figures is our values in the beginning were reported with an accuracy of three significant figures. If you go back here, all these values in the given section are three significant figures. So that's the most accurate we can report to. Okay, now going to be that b was this time, eh? Plus B minus c. Okay, Pan has before we're gonna do this for a plus. B minus C. What? This is Freddy X close, eh? Plus B might have C for the why. Okay. And if you look above, we have ah values for the ex component baby and seeing the white component of a B and C written there. But now we're going to change whether or not they're added. Of course, attracted. So you have 38 0.5, and this is going to be a plus. Welk plus minus 14 8.2. So plus and minus is just minus minus 14.2. Okay. And this isn't the extraction, and this is plus and also note again. See, of ex zeros. There's no sea of ex Mrs Plus 2026 6 And then plus this time 21.97 Right. And then this time it's minus minus 31. Well minus a minus is a plus. Sosa's plus 31. That's why. Yeah, and then you carry this out. This is equal to 24. I began. This is the I had correction and then plus no, my Andy. That plus 73.6 Jay had correction box. That ends your solution. Okay. And lastly, we need to do part c. So rewrite part. See? Report. See, Was C minus a minus B. Because you're all back tears kick. Well, that's C minus. A minus B. Ex direction plus C minus A minus. B Kwai direction. Okay, well, see Chrissy x zero, this is 38.5. So that's minus 38. This is recognizable. Here we go. 38 25 minus B, which the was minus 14.82 So minus and minus is a plus. 14.82 Yeah, this is the extraction. Plus, we're gonna do this for the Y direction now. So see is minus 31 minus a and the Y direction was 26 point or 20.66 So it's minus 20 0.66 Okay. And then minus B B in the white direction was 21.97 So this is going to be minus 21 0.97 Yeah, that's good direction. Hey, if you go ahead and carry this out, you will see that It's minus 24. Mrs E. I had direction. Plus I'm sorry. Minus 73.6 this time that is in the J had directions Fox that in your solution her c.

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