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?
We can determine the magnitude with the Pythagorean Theorem. In this case, 2^2+3^2=c^2 so 4+9=c^2 and c=3.6
In order to determine the angle counterclockwise from the positive x axis, we can draw the triangle and label the sides. We know that the two legs are 2 and 3, and the angle formed where they meet is 90 degrees. The remaining angles must equal 90 degrees, and their measures are proportional to the length of their opposite sides. We can say that 2a+3a=90, or a=15. Since 2a=< opposite x axis, and 3a = < opposite y axis, we know that the two angles are 36 degrees and 54 degrees respectively. The 54 degree angle is the angle measured counterclockwise from the positive x axis.
• What are the components of the equilibrant force?
The components of the equilibrant are: x component = -2 N, y componenet = -3N
• What angle does the equilibrant force make as measured counterclockwise from the positive x axis?
To determine this angle, we can add 180 degrees to the 54 degrees of the original angle, to get 234 degrees.
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20 min
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Very good. Let me know if you have any questions.