1. Fa is a force vector with a magnitude of 10.0 N and makes an angle of 25.0 de
ID: 2003777 • Letter: 1
Question
1. Fa is a force vector with a magnitude of 10.0 N and makes an angle of 25.0 degrees with the x-axis. Fb is a force vector with a magnitude of 5.00 N and makes an angle of 45.0 degrees with the x-axis. Use the mathematical method to find the resultant of Fa and Fb.
2. The force vector Fc acts on a body, along with the forces Fa and Fb given in problem 1. Fc has a magnitude of 15.0 N and acts in the first quadrant at an angle of 10.0 degrees to the y-axis. Use the polygon method to solve for the resultant of these three factors.
Explanation / Answer
Draw the first vector from the origin 10 N long @ 25°. From its tip, draw the 2nd vector 5 N long @ 45°.
Since the difference in the angles is 20°, you have a triangle with sides 10 & 5 with the included angle = 160°. Solve for the magnitude of the 3rd side using the law of cosines:
R = [10² + 5² -2*10*5*cos160°] = 14.8 N
Let ' be the angle of the triangle at the origin. Then
' = arcsin[5*sin160°/14.8] = 6.636° (law of sines) and the angle R makes with the x axis:
= 25 + ' = 31.636°
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