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TrojanPoem
 one year ago
Mechanics
TrojanPoem
 one year ago
Mechanics

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TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444160889035:dw

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0F_2 = 186.3 / 98.8 / 47.7 / 72.2 beta = 303.6 / 123.6 / 236.4 / 56.4

phi
 one year ago
Best ResponseYou've already chosen the best response.1what does 120 N R= 180 N mean ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0The direction of the resultant is the same as the force 120

phi
 one year ago
Best ResponseYou've already chosen the best response.1What two vectors are we adding to produce the resultant ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0It's the result of adding all the forces

phi
 one year ago
Best ResponseYou've already chosen the best response.1so we are adding 4 vectors? in terms of mag, angle <170, 50> <F2, beta> <200, 180> <120, ??> do we have to find the angle for that last vector ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0The triangle is drawn

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0In mechanics they mostly draw the triangle on the line like this:dw:1444162046880:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, so we need the angle. what is it ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444162127993:dw

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0We are looking for beta and F_2

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, here are the 4 vectors <170, 50> <F2, beta> <200, 180> <120, 126.87> and the result is <180, 126.87> correct?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0Will you use beta ? as anti clockwise ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1I would write down each vector in <x,y> components and add them up.

phi
 one year ago
Best ResponseYou've already chosen the best response.1Here are the details change to rectangular coords <x,y> using <r cos A, r sin A> where <r,A> are polar coords we get <170, 50> > <109.27, 130.23> <F, A> > < F cos A, F sin A> <200, 180> > <200, 0 > <120, 126.87> > < 72, 96 >  <180, 126.87> > <108, 144> add up the 4 vectors, by adding the their x components and their y components, and set equal to the resultant's components we get F cos A  162.72= 108 F sin A + 226.23= 144 or F cos A = 54.73 F sin A = 82.23 vector F in rectangular coords is <54.73, 82.23> in polar coords A = atan( 82.23/54.73) = 56.35 deg F= sqr( 54.73^2 + (82.23)^2 ) = 98.78

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0@phi , dw:1444238623491:dw 170Cos50 + F_2Cosbeta  120 * 3/5  200 = 3/5 * 180 ( resultant component in xaxis) F_2CosBeta = 54.73 170Sin50 + 120 * 4/5  F_2SinBeta = 180 * 4/5 ( resultant component in y  axis) F_2SinBeta = 82.23 TanBeta = 82.23/54.73 <(beta) = 360 56 21 = 303.6 F = 82.23/sin303.6 = 98.8 F = 54.73/ cos303.6 = 98.8 OK, where is the mistake ? I keep getting ve , +ve values for the same force :/ help !

phi
 one year ago
Best ResponseYou've already chosen the best response.1You have **170Sin50 + 120 * 4/5  F_2SinBeta = 180 * 4/5*** I would use 170Sin50 + 120 * 4/5 + F_2SinBeta = 180 * 4/5 so you get F_2 Sin Beta= 82.23

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0@phi , But why did you change the sign to +Ve ? Sin(360 beta) = Sinbeta ? If so why can't I use the normal beta, I am breaking the force into its components.

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0I was told to use the anticlockwise angle when giving out answers not breaking the force.

phi
 one year ago
Best ResponseYou've already chosen the best response.1My thought to use beta is wrong. We should use Beta and solve for it. we will get 303 which also can be written as 57. The important thing is r cos beta and r sin beta give the correct magnitude and direction of each component. from the diagram we know x is positive and y is negative.

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0So the negative here points to the direction of the force component ( ve y axis ) ? so it's not wrong that the force gives two signs ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1the magnitude F2 should always be positive notice if we use 82 , we will get a positive value for F2 using 82/sin 303

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0F_2SinBeta = 82.23 I have 82 as positive, what did I do wrong ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1when you solve for F_2 and Beta, use the terms r cos beta and r sin beta (you used r sin beta for the y value)

phi
 one year ago
Best ResponseYou've already chosen the best response.1in other words, let's not overthink this. the components are always r cos A , r sin A (no A angles!)

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0I used  r sin beta as I assumed that the resultant direction is on the +ve y axis so anything in +ve y axis = + , anything in ve y axis = ve

phi
 one year ago
Best ResponseYou've already chosen the best response.1no, we vectors that have magnitude r and direction beta. we should just use r and beta.

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0If we used direction beta, we would use the anticlockwise angle , right ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0I think using your method of solving them would be easier.

phi
 one year ago
Best ResponseYou've already chosen the best response.1if we convert from polar to rectangular we get <170, 50> > <109.27, 130.23> <F, A> > < F cos A, F sin A> <200, 180> > <200, 0 > <120, 126.87> > < 72, 96 >  <180, 126.87> > <108, 144> add them up we get F cos A  162.72= 108 F sin A + 226.23= 144 F cos A = 54.73 F sin A = 82.23 if we divide the bottom equation by the top we get \[ \frac{F \sin A}{F \cos A}= \frac{ 82.23}{54.73} \\ \tan A = \frac{ 82.23}{54.73} \] notice the y value is neg and the x value is pos, that means we are in the 4th quadrant. if we square both equations we get \[ F^2 \cos^2 A = (54.73)^2 \\ F^2 \sin^2 A = (82.23)^2 \] add them to get \[ F^2 \cos^2 A + F^2 \sin^2 A =(54.73)^2 + (82.23)^2 \\ F^2(\cos^2 A +\sin^2 A)=(54.73)^2 + (82.23)^2 \\ F^2 = (54.73)^2 + (82.23)^2 \\ F= \sqrt{(54.73)^2 + (82.23)^2}\]

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0Squaring both sides, really ingenious idea. Cos^2A + Sin^2A = 1 That way we can find the force first thanks :)

phi
 one year ago
Best ResponseYou've already chosen the best response.1that is the background on how to change from rectangular to polar (x,y) A= atan(y/x) r= sqr(x^2 + y^2) you can also do r= x/cos A or r= x/sin A

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I took " rectangular to polar" before, I think in imaginary numbers.

phi
 one year ago
Best ResponseYou've already chosen the best response.1are you posting a different question ?
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