Cartesian Vector Addition 1 of 7> Learning Goal: To find the resultant of multip

Question

Cartesian Vector Addition 1 of 7> Learning Goal: To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. F, =-50 i + i05 j + 45 k ib. F, = 110 lb and forms the following angles with the x, y, and z axes, respectively: = 52.7" , = 70.1° . and 136.0° . F3 = 110 lb, forms the angle Part A-Resultant of adding F1 and F3 Find the resultant of adding Fi and Fs. Express your answer in component form. Express your answers, separated by commas, to three significant figures. View Available Hints) 30° with the z axis, and forms the angle 0- 29° between the x axis and the projection of Fs in the zy plane. ilb.j lb, k lb F, Submit Fi Part B-Resultant of adding F1 and F2 and F3 Find the resultant of adding Fi. Fa. and Fs. Express your answer in component form Express your answers, separated by commas, to three significant figures View Available Hint(s) F, vec

Explanation / Answer

Ans:-

F1 = -50i + 105j +45k lb ………………..1

F2= 110lb, =52.7,= 70.1 ,= 136

F2 = 110cos52.7 i + 110cos70.1 j+ 110cos136k

F2 = 66.7i + 37.4j -79.1k…………………..2

F3 =110lb =30 =29

F3 = 110cos29i +110cos30K

F3 = 96.2i +95.3K……………………3

PartA R13 = F1 +F3

= 46.2i +105j + 140.3k

R13 =46.2ilb , 105jlb,140.3klb

PartB R123 = F1 + F2 +F3

=112.9i + 142.4j +61.2k

R123 = 112.9ilb , 142.4jlb , 61.2klb

Part C R123 = 112.9i + 142.4j +61.2k

R = sqrt (112.9^2 + 142.4^2 + 61.2^2 ) = 191.8

R = cos-1 (112.9/191.8) = 53.9 deg

R = cos-1 (142.4/191.8) =42.1deg

R = cos-1 (61.2/191.8) = 71.39deg

Part D R=39.5, R= 65.5

Using relation cos^2R + cos^2R + cos^2R = 1

CosR = sqrt (1-(cos^2R + cos^2R))

          =sqrt(1-(0.7716^2 + 0.4147^2))

           =0.4824

R= 61.16deg

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