Answer to Question #222024 in Civil and Environmental Engineering for syra

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
1
Expert's answer
2021-08-09T08:04:08-0400


In unit vector form

Fx=20cos3040cos6025+12cos45=19.194NFy=20sin3040sin6042+12sin45=5.844NF=Fx2+Fy2F=(19.194)2+(5.844)2F=20.064Nα=tan1(5.84419.194)α=16.9340F_x = 20 cos 30 - 40 cos 60 -25 +12 cos 45 = - 19.194 N\\ F_y = 20 sin 30 - 40 sin 60 -42 +12 sin 45 = - 5.844 N\\ F= \sqrt{F_x^2+F_y^2}\\ F= \sqrt{(-19.194)^2+(-5.844)^2}\\ F= 20.064 N\\ \alpha = \tan^{-1}(\frac{-5.844}{-19.194})\\ \alpha = 16.934^0\\

Therefore, the angle is 1800+16.9340 = 196.9340

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