Two forces, and , act at a point, as shown in the picture. has a magnitude of 8.

Question

Two forces, and , act at a point, as shown in the picture. has a magnitude of 8.20 and is directed at an angle of = 61.0 above the negative x axis in the second quadrant. has a magnitude of 7.00 and is directed at an angle of = 52.2 below the negative x axis in the third quadrant.
a.What is the x component of the resultant force?
b.What is the y component of the resultant force?
c.What is the magnitude of the resultant force
d.What is the angle that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative axis.

Explanation / Answer

(a) the x component of the resultant force is [-8.20* cos(61 degree) ] + [-7.00*cos(52.2 degree)] = -8.266 (b) the y component of the resultant force is [8.2*sin(61)] + [-7*sin(52.2)] = 1.641 (c) magnitude of resultant force = sqare root of { [x component]^2 + [y component]^2 } mag = [(-8.266)^2+1.641^2]^0.5 = 8.427 (d) the angle would be arc tangent[absolute value of(y component/x component)] arctan(1.641/8.266) = 11.23 degree above the negative x axis in the second quadrant.

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