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PHY 121
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The equilibrant of a force is the force which is equal and opposite to that force. If two forces are equal and opposite, their x and y components are also equal, but the x and y components of the force are opposite in sign to those of the equilibrant.
The x and y components of a force are 2 Newtons and 3 Newtons repectively.
What are the magnitude of this force and what angle does it make as measured counterclockwise from the positive x axis?
magnitude: a^2 + b^2 = c^2
(2 N)^2 + (3N)^2 = c^2
4 N^2 + 9 N^2 = c^2
13 N^2 = c^2
c = 3.6 N
angle: tan-1 (3/2) = 56 degrees
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What are the components of the equilibrant force?
-2 N and -3 N
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What angle does the equilibrant force make as measured counterclockwise from the positive x axis?
tan -1 (-3/-2) = 56 degrees
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The equilibrant is in the direction opposite the force, so it can't have the same angle.
The angle of any vector measured counterclockwise from the positive x axis is
arcTan( y comp / x comp), plus 180 degrees if the x component is negative.
So the angle is 56 deg + 180 deg = 236 deg.
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