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Find the work done by F = (-2,5,1) (FFI V3O N) in moving an object along the straight line from ( - 1, 1,-2) to ( - 5,4,2)WorkIJoules...

Question

Find the work done by F = (-2,5,1) (FFI V3O N) in moving an object along the straight line from ( - 1, 1,-2) to ( - 5,4,2)WorkIJoules

Find the work done by F = (-2,5,1) (FFI V3O N) in moving an object along the straight line from ( - 1, 1,-2) to ( - 5,4,2) Work IJoules



Answers

Find the work done by a force $\vec{F}=1.8 \hat{\imath}+2.2 \hat{\jmath} \mathrm{N}$ as it acts on an object moving from the origin to the point $56 \hat{\imath}+31 \hat{\jmath} \mathrm{m}$.

Consider the provided statement to find the world burned by the victor. Appeal. Careful X Coma by Kamanzi as equals Toe X in tow. I Victor Last three expire in two day victor minus express Z in do deodorant along the line segment from the point one comma will commit to to the point zero comma five coma one now the better My prick equation off the line segment from the 0.1 comma ball coming to the 0.0 comma five Kermabon is I don't be as equals to one minus t in Do van comma for comma plus t into zero comma five Marvel by using the distributed multiplication property. Get one minus day coma old minus four would be coma tu minus droopy last wifey coma The That's all the best we get one minus t Well, now four plus D Oh, my through dynasty. There he is greater than equals to you and smaller than the Quest one. Now the first order derivative off Rop is our brandy is equals to minus one. Cool Maman called my mind. This one the What done? By the way, computer iss. A full rop is equals toe one minus D into I picked two last three into one minus t into or Presti in direct for minus one minus. T plus two minus t into the victor, which is equals toe one, minus d And do I make? Yes. Well of minus 90 minus three. B squad in the director, minus three minus to be into it. I have done. But the big tribute is tightly, dude, as in to go see a full beyond is equal store integral zero Boban. Careful. I won't be. And do our Frankie Todt mass obstructive in the values we give Integral as you want. One minus D pinto I, Victor less well minus 90 minus three. T square into director minus three minus to B into giving Indu minus I, Victor plus de Victor minus K Victor and to the muscle that this be good. Indigo's you one. Minus what? Rusty. Bless with minus nine B minus three piece crab minus minus pre minus to B in Jodi, but does equals toe. Indeed. A 0 to 1 minus dainty. 14 minders three T square in tow. 90. Grab. Integral of this function is minus. They'd be where are divided by two class for the Indy minus three. Take you divided by three, then the limit of 0 to 1 that's obstructing picked up and no lower limit. We get minus fight plus for being minus one, which is equals two week, the world done by the big true field as

Okay, we're going to find the work done by a force of one newton that's acting in the direction of to I plus two J plus K. Um and then we're in order to work that's our force. And then our displacement is going to be our displacement of going from 000 to 1-2. So our displacement of vectors is nice to find. Um But what we're going to be doing is we want to be able to find our dot product. And so that we have the information of kind of how to do that projection so that we can really figure out what part of our force vector is actually going in the direction of displacement. Because work is all about force in the direction of displacement multiplied by displacement. So we are going to be doing a dot product. We are going to have to find our um the magnitude of that direction. And um in order to um do that, you know, we will write that direction vector. So we've just done the differences, fortunately it's zero. So that makes things easy. Okay, so my magnitude of my vector V. And the reason why I have to do this is because it's just giving me the direction, it's not really giving me my actual for spectre. I have to come up with that. So it ends up the square root of nine is three. And so now we do at least know the magnitude of our vector V. We also need to know the magnitude of our vector W. Which also happens to be square root of nine, which is three. So because of that um we're gonna go ahead and write our force vector as two thirds I plus two thursday I just noticed a multiple. I'm dividing every component by three. And then if we want to now find that projection, we need our dot product. So we're using that vector V. So we have the two thirds times won the two thirds times two and the one third times two. And we add them all together, we get a dot product of 3/8. So we'll take that 3/8. And we're going to be dividing by our um w. And so our projection is um so out of that hole, one newton, we're gonna be using 8/9 of that newton. And then um considering that we're going a direction of um a distance of three. So we multiply those together, we get that 8/3. And when you do a newton times a meter, you get a jewel. So that J stands for jewel. But you can write newton times meter if you like.

Were given a force and a path. And we're has to find the work done by this force across this path. Force Yes. Is X Y I plus y minus X jay. And the path is the straight line. Right from the 0.11223 Falsehoods and misinformation. First, let's find a privatization for this path. Well, the pack contains the 0.11 and has a direction Vector. This which is two minus one, is one and three minus. One is two and therefore they can be premature ized as r t equals, we start out our X coordinate is one plus. Mm. Yes, one times T i plus our Why coordinate? Which is our starting 0.1 plus two times t jay. And we let t range from zero up to one. And therefore, our prime of T is equal to one I plus two j and the work done by the force not only over the straight line. This is the line integral of f dotted with d R over this path, which is the integral from T equals 0 to 1 of our force in terms of our path. So we have X times y This is one plus t times one plus two t i plus y minus x which is true one plus two t minus one plus T jay Super dotted with D r, which is just our prime. This is I plus two J d t mhm. This simplifies to the integral from 0 to 1 of one plus three t plus two t squared I plus one minus one is zero to t minus. T is just from going through T Jay take dotted with I plus two j d. T. This is equal to the integral from 0 to 1 of one plus three t plus two t squared plus two t d t yeah, and then taking anti derivatives. This is C T plus what? We have five tes This is five halves and so t squared, plus two thirds t cubed from t equals 0 to 1 mhm. And this is simply one plus five halves plus two thirds. This is equal to 25 6th.

Were given a vector field F and rest to calculate the work against F required to move an object from the 0.112 point 34 along any path in the first quadrant. So our vector field F is one over X negative one over. Why now? Let's take potential energy function v of x y to be the natural log of X minus the natural log of y. We're sorry. Let's take it to be the natural log of y minus the natural log of X. Then we see that the Grady INTs V is the opposite of that so that F is equal to the opposite of the Grady INTs of the therefore. F is a conservative force field now, because it's conservative. We cannot make a statement about the work required to move an object between these points along any path. So the work against F or any path this is the line integral over this curve, connecting these two points of F sheets the opposite of this since we're working against deaf and this is our potential function. V evaluated at the terminal points 34 minus be evaluated at the initial 0.11 of the curve substituting. This is the natural log of four minus the natural log of three minus the natural log of one minus natural log of one which is natural log of four minus the natural log of three.


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