Two forces, F ? 1 and F ? 2, act at a point, as shown in the picture. (Figure 1)

Question

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.80N and is directed at an angle of ? = 65.0? above the negative x axis in the second quadrant. F? 2 has a magnitude of 5.20N and is directed at an angle of ? = 53.9? below the negative x axis in the third quadrant.What is the magnitude F of the resultant force?What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.80N and is directed at an angle of ? = 65.0? above the negative x axis in the second quadrant. F? 2 has a magnitude of 5.20N and is directed at an angle of ? = 53.9? below the negative x axis in the third quadrant.What is the magnitude F of the resultant force?What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Explanation / Answer

sum in the x

Fx=-F1 cos alpha - F2 cos beta = -9.8*cos(65 degrees) - 5.2*cos(53.9 degrees)= -7.21 N

now for y

Fy = F1 sin alpha - F2 sin beta = 9.8*sin(65 degrees) - 5.2*sin(53.9 degrees) = 4.68 N

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