Question

You are an engineer tasked with making sure that this problem is solved correedy. There ane hree force vectors acting on an object (a) [2 points] Sketch an x-y coordinate and label all three vectors with the following attributes: A has a magnitude of 1054 N at an angle of 138° as meas ured counter-clockwise from the positive x-axis. B has a magnitude of 642 N at an angle of 35" as measured counter- clockwise from the positive x-axis. C has a magnitude of 500 N in the negative y direction (b) [4 points] Find the x- and ycomponents of a 4h force, D, so that the net force acting on the object is zero (c)12 points] What is the mgntude of D? (d) [2 points] What is the direction of D, as an angle measured counter-clockwise from positive x-axis?

Answer 1

A vector = -1054 sin 48 i^^+ 1054 cos 48 j^^ B vector = 642 cos 35 i^^+ 642 sin 35 j^^ C vector = 0i^^-500 j^^ A vector + B vector + C vector = (-783.27 + 525.89) i^^+ (705.26 + 368.23 - 500) j^^ A vector + B vector + C vector = -257.38 i^^+ 573.49 j^^ D vector = 257.38 i^^-573.49 j^^N D_x = 257.38 i^^N D_y = -573.49 j^^N Vertical-bar D vector Vertical-bar = squareroot (257.38)^2 + (573.49)^2 = squareroot 66244.46 + 328890.78 Vertical-bar D vector Vertical-bar = 628.59 N rightarrow Answer tan theta = F_x/F_y tan theta = 257.38/573.49 theta = 24.17 degree Total angle = 270 + 24.17 Total angle = 294.17 degree