Question #222024

Compute the direction and magnitude of the resultant of the following system of coplanar and concurrent forces; 20 N, 40 N, 25N, 42N, and 12 N making an angle of 30

Expert's answer

In unit vector form

"F_x = 20 cos 30 - 40 cos 60 -25 +12 cos 45 = - 19.194 N\\\\\nF_y = 20 sin 30 - 40 sin 60 -42 +12 sin 45 = - 5.844 N\\\\\nF= \\sqrt{F_x^2+F_y^2}\\\\\nF= \\sqrt{(-19.194)^2+(-5.844)^2}\\\\\nF= 20.064 N\\\\\n\\alpha = \\tan^{-1}(\\frac{-5.844}{-19.194})\\\\\n\\alpha = 16.934^0\\\\"

Therefore, the angle is 180^{0}+16.934^{0} = 196.934^{0}

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