A force vector, F 1 = 11.5 N makes an angle = 55.6° with the +x-axis and another

Question

A force vector, F1 = 11.5 N makes an angle = 55.6° with the +x-axis and another force vector,F2 = 11.0 N makes an angle = 149.9° with the+x-axis. What is the sum of the x components ofF1 and F2? What is the sum of the y components ofF1 and F2? What is the magnitude of the sum of F1and F2? What is the angle the sum ofF1 and F2 makes with the +x-axis? A force vector, F1 = 11.5 N makes an angle = 55.6° with the +x-axis and another force vector,F2 = 11.0 N makes an angle = 149.9° with the+x-axis. What is the sum of the x components ofF1 and F2? What is the sum of the y components ofF1 and F2? What is the magnitude of the sum of F1and F2? What is the angle the sum ofF1 and F2 makes with the +x-axis? What is the angle the sum ofF1 and F2 makes with the +x-axis?

Explanation / Answer

F1x = F1 * cos = 11.5 N * cos 55.6 = 6.50 N F2x = F2 * cos = 11.0 N * cos 149.9 = -9.52 N Fx = F1x + F2x = -3.02 N F1y = F1 * sin = 11.5 N * sin 55.6 = 9.49 N F2y = F2 * sin = 11.0 N * sin 149.9 = 5.52 N Fy = F1y + F2y = 15.0 N F=F1+F2 |F| = (Fx^2 + Fy^2) = 15.31 N = angle(F) = atan Fy/Fx = 101.38 deg For the last step it is important to visualize the location of theresulting vector: F=(-3.02,15.0)N is in the 2nd quadrant. Therefore must be between 90 and 180 degrees. If necessary, one needsto add 180 degrees to the result returned by a calculator to get apositive angle .

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