A charged object has two forces acting on it: F1 (4 Newtons, pointing up at 120

Question

A charged object has two forces acting on it: F1 (4 Newtons, pointing up at 120
degrees from the positive x axis), and F2 (8 Newtons, pointing down -30 degrees from the positive x-axis).
(a) Write down F1and F2 in terms of the unit vectors i (along x-axis) and j (along the y-axis).
(b) Compute the total (net) force acting on the object and write it down in terms of i and j.
(c) Write down the total force in polar form, i.e. give its magnitude (in Newtons) and its orientation (angle from the positive x-axis)

Explanation / Answer

a)F1 = 4cos120i+4sin120j = (-2i+23j)N

F2 = 8cos-30i+8sin-30j = (43i-4j)N

b)net force = F1+F2 = (-2i+23j)+ (43i-4j) = (43-2)i+(23-4)j

c) magnitude = ((43-2)2+(23-4)2) 4.95 N

orientation = tan-1((23-4)/(43-2)) = -6.204o

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