problem on the picture please use any x y cartesian coordinate system where x is

Question

problem on the picture please use any x y cartesian coordinate system where x is horizontal positive to the right and y is vertical , positive upward. if the answer requires vector expression, report the vectors using cartesian representations.

A utility pole supports a bundle of wires that apply the 400 and 650 N forces shown, and a guy wire applies the force P. P = 0, determine the resultant force applied by the wires to the pole and report your result using polar vector representation. Repeat Part (a) if P = 500 N and alpha = 60degree. With alpha = 60degree. what value of P will produce a resultant force that is vertical? If the resultant force is to be vertical and P is to be as small as possible, determine the value alpha should have and the corresponding value of P. Figure P2.18

Explanation / Answer

a)   reaultant force Fnet = 400cos30i + 400sin30 j - 650 i

     = -303.59 i + 200 j N

magnitude = srqt(303.59^2 + 200^2) = 363.55 N

angle = 180 - tan-1 (200/303.59) = 146.62 degrees from x in counterclockwise

so Fnet = 363.55cos146.62 i + 363.55sin146.62 j

b) Fnet = -303.59 i + 200 j + 500cos60i - 500sin60 j

           = -53.59 i - 233.01 j N

magnitude = sqrt(53.59^2 +233.01^2) = 239.10 N

angle = 180 + tan-1(j/i) = 257.05 dgerees

so Fnet = 239.10cos257.05 i + 239sin257.05 j   N

c) then Pcos60 = 303.59

P =607.18 N

d) Pcos(alpha) = 303.59

P - min   cosalph = max = 1

alpa = 0 dgree.

P = 303.59 N

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