Answer to Question #141420 in Mechanics | Relativity for Holden Giles Cabrito

Question #141420
A force of magnitude 200 N is directed West, and a second force of magnitude 100 N is directed East of
North. Find the magnitude and direction of a third force that, when added to the first two forces, gives a
resultant whose magnitude is zero.
1
Expert's answer
2020-10-30T13:17:40-0400

Answer

F1=200NF2=100NF_1=200N\\F_2=100N

Assuming that F2 is 30° east of North

resulant force in x -direction

Fx=200100sin30°=150NF_x=200-100sin30°\\=150N

Force in vertical direction

Fy=100cos30°=86.6NF_y=-100cos30°=-86.6N

Resulatant force

FR=Fx2+Fy2F_R=\sqrt{F_x^2+F_y^2}


FR=1502+86.62=173.2NF_R=\sqrt{150^2+86.6^2}=173.2N

Angle

tanθ=86.6150θ=30°tan\theta=\frac{-86.6}{150}\\\theta=-30°

So third force of 173.2N should be applied -30° below horizontal or 60° east of South.













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