? 3-30 ? Ax Ayl ? By ?By ? (a) From ? (By)/(π D^2) = (2000...

? 3-30 ? Ax Ayl ? By ?By ? (a) From ? $\frac{B_y}{\pi D^2}$ = $\frac{2000 lb}{\pi D^2 L}$ By = 2000 lb x $\frac{1}{9}$ = 222.22 lb From 1 ?+?M = 0 By x 11 - F x 16 = 0 F = $\frac{B_y}{16}$ = $\frac{222.22}{16}$ F = 13.89 lb (b) U? = U? F?l? = F?l? 13.89 lb x 5 in = 2000 lb x d? d? = 0.035 in

Transcript

00:01 In this problem, we have been given to convert polar equation into a cartesian equation.

00:05 Let us see how we can do that.

00:06 So, first of all, we must know some formulas over here that are useful for changing.

00:13 That is, cosine of theta is equals to x over r.

00:17 And then here we have sine of theta equals y over r.

00:22 And then we have x square.

00:25 So this x, sorry, this is r square.

00:28 So r square will be equals to x square plus y square.

00:32 So with these three formulas, we will try to convert our first equation given in the problem.

00:38 So first equation is like r equals 2 cost theta plus 3 sine theta.

00:49 So with this particular equation, so here we have 2 cost sine theta and then we have 3 sine theta.

00:57 So we can write this one more clearly.

01:00 And now we can write that r will be equals to 2 multiplied x over r.

01:06 We are just using these formulas.

01:08 These formulas are very helpful to solve such kind of problems.

01:12 So here we can write that 3 multiplied y over r.

01:15 So r square will be what? r square will be 2x plus 3y.

01:21 Now the r square value can be converted to x square plus y square.

01:26 So we have 2x plus 3y.

01:30 So we have almost solved the problem.

01:33 Now we have some more process to apply on it.

01:37 Like we can try the process of completing the square because we are here having 2x.

01:44 Just we replaced or we can say like that we have just added and subtracted both the sides with minus 2x.

01:54 And hence we have minus 2x.

01:56 1 minus 1 plus here we will have y square minus 3y and here we can write like plus 3 by 2 3 over 2 square minus 3 over 2 square equals to 0 so with this particular completing the square method we can write that this will be equals to x minus 1 whole square plus y minus 3 over 2 whole square and these are not will be equals to 1 plus 9 over 4 and this is equals to 13 over 4 so this is the final answer for our first part in which we can write that answer is x minus 1 square plus y minus 3 over 2 square equals how much will it be it will be 13 over 4 now let us look into our into the second part of the problem so in the second part we have been given different uh different equation and that equation looks like we can write that one as r square sign of 2 theta equals 2a square so with this particular formula let us see how we can solve it so we can just break the sine 2 theta into two parts so what parts they will be they will be like r square multiplied 2 sine theta and then here it will be cause of theta this is the formula for double angles and here it will be equals to 2a square so first of all this 2 and 2 get cancelled out from lhs and rhs and then this r square and here we have sine theta so sine theta will be equals to y over r and then here it is x over r so we can just show the multiplication sign with dot because it looks awkward to show it with the cross sign...

Question

? 3-30 ? Ax Ayl ? By ?By ? (a) From ? $\frac{B_y}{\pi D^2}$ = $\frac{2000 lb}{\pi D^2 L}$ By = 2000 lb x $\frac{1}{9}$ = 222.22 lb From 1 ?+?M = 0 By x 11 - F x 16 = 0 F = $\frac{B_y}{16}$ = $\frac{222.22}{16}$ F = 13.89 lb (b) U? = U? F?l? = F?l? 13.89 lb x 5 in = 2000 lb x d? d? = 0.035 in

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