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 3 Baseline Overscript right-arrow EndScripts such that the vector sum of the three forces is 0 N? theta in the drawing) of the third force Upper F Subscript 2 Baseline Overscript right-arrow EndScripts has a magnitude of 14.3 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle Upper F Subscript 1 Baseline Overscript right-arrow EndScripts has a magnitude of 22.8 newtons (22.8 N) and is directed 30.0½ to the left of the +y axis. Force

Explanation / Answer

F1x = -(22.8*sin30) = -11.4 N

F1y = 22.8*cos30 = 19.74 N

F2x = 14.3

F2y = 0

a)

Fx = F1x + F2 + F3x

Fx = 0

F1x + F2 + F3x = 0

-11.4 + 14.3 + F3x = 0

F3x = -2.9 N

Fy = F1y + F2y + F3y

Fy = 0

F1y + F2y + F3y = 0

19.74 + 0 + F3x = 0

F3x = -19.74 N

magitude = sqrt(F3x^2 + F3y^2) = 19.95 N <------answer

b)

direction tan^-1(Ffy/Fx) = 81.62 below the -x axis

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