Three forces are applied to an object, as shown in the figure. Force Upper F Sub

Question

Three forces are applied to an object, as shown in the figure. Force Upper F Subscript 1 Baseline Overscript right-arrow EndScripts has a magnitude of 20.3 newtons (20.3 N) and is directed 30.0° to the left of the +y axis. Force Upper F Subscript 2 Baseline Overscript right-arrow EndScripts has a magnitude of 14.9 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle theta in the drawing) of the third force Upper F Subscript 3 Baseline Overscript right-arrow EndScripts such that the vector sum of the three forces is 0 N?

Explanation / Answer

Fnet = F1+F2+F3

Fnetx = F1x+F2x+F3x

0 = -20.3sin30 +14.9cos0+ F3x   => F3x = -4.75 N

Fnety = F1y+F2y+F3y

0 = 20.3cos30 +14.9sin0+ F3y   => F3y = -17.58 N

F3= -4.75 N i^ -17.56 N

a)   |F3| = sqrt(F3x^2+F3y^2) = sqrt[(-4.75)^2 + (-17.58)^2] = 18.21 N

b) Direction, = tan^-1 (F3y/F3x) = tan^-1[(-17.58)/( -4.75)] = 74.88 deg   left of the -x axis

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