cq_1_191

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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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