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phy 121
Your 'cq_1_19.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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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?
To find the magnitude we use what we have learned from our good man Pythagoras,
Magnitude = `sqrt 2n^2 + 3N^2 = 3.6N
Angle = tan-1 (3n/2n) = 56.3 degrees
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• What are the components of the equilibrant force?
According to the above the x and y components of the force are opposite in sign to those of the equilibrant, so the equilibrant magnitude will be
Magnitude = `sqrt -2n^2 + (-3N^2) = -3.6 ???I’ve mentioned it previously but my calculator says 3.6i which is apparently the proper way of writing the square root of a negative number???
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i stands for the square root of -1. But the i arose in your calculation from an error with order of operations.
The magnitude of <-2 N, -3 N> is sqrt( (x comp)^2 + (y comp)^2 ), which in this case is
sqrt( (-2 N)^2 + (-3 N)^2)
(-2 N)^2 = (-2)^2 N^2 = 4 N^2, not -4 N^2
Similarly for the square of -3 N.
So the magnitude is
sqrt( (-2 N)^2 + (-3 N)^2)
= sqrt( 4 N^2 + 9 N^2)
= sqrt(13 N^2)
= sqrt(13) sqrt(N^2)
= 3.6 N.
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I believe to find the angle we need to add 360 to whatever number we get since we have a negative y component, but for a negative x component we add 180. Im not sure what the rule is for both a negative x and y component, I will show both.
Angle = tan-1(-3N / -2n) = 56 actually this should be okay since the negative numbers divide out to be a positive number , but perhaps this angle is also supposed to be negative since the equilibrant has opposite signs of the components.
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• What angle does the equilibrant force make as measured counterclockwise from the positive x axis?
Possible answers I have:
56 degrees
-56 degrees (equilibrant is opposite sign)
-56+ 180 = 124
-56+360 = 304
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20 minutes
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Good, but check my note on that 3.6 i result. You made an error with the order of operations and got an imaginary number.
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