Answer to Question #249701 in Physics for Laxus

Question #249701

A = 50 N @ 30 degrees N of E

B = 110 N @ 40 degrees  N of W

C = 75 N @ 60 degrees  S of W

D = 130 N @ 20 degrees  S of E



From

the given vector quantities above, 



a. illustrate the vectors

b. determine the summation of X

c. determine the summation of Y

d. determine the resultant vector

e. determine the angular position of the resultant vector

f. determine the directional position of the resultant vector

g. complete the magnitude and direction of the resultant vector

h. determine the equilibrant force


1
Expert's answer
2021-10-11T11:00:46-0400

a.


b. Summation of X:

"R_x=130\\cos20\u00b0+50\\cos30\u00b0-110\\cos40\u00b0-\\\\-75\\cos60\u00b0=43.7\\text{ N}."

c. Summation of Y:

"R_y=-130\\sin20\u00b0+50\\sin30\u00b0+110\\sin40\u00b0-\\\\-75\\sin60\u00b0=-66.2\\text{ N}."

d. Resultant:

"R=\\sqrt{R_x^2+R_y^2}=79.3\\text{ N}."

e. Angular position:

"\\theta=\\arctan\\frac{R_y}{|R_x|}=33.4\u00b0\\text{ East of South}."

f. Directional position:


"\\vec R=(43.7\\hat\\textbf i-66.2\\hat\\textbf j)\\text{ N}."

g. Magnitude and direction:

"\\vec R=79.3\\angle(360\u00b0-33.4\u00b0)=79.3\\angle326.6\u00b0\\text{ N}"

h. The force is

"F_R=79.3\\angle(326.6\u00b0-180\u00b0)=79.3\\angle146.6\\text{ N}."


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