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

Question

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.

Answer 1

Answer

$F_1=200N\\F_2=100N$

Assuming that F₂ is 30° east of North

resulant force in x -direction

$F_x=200-100sin30°\\=150N$

Force in vertical direction

$F_y=-100cos30°=-86.6N$

Resulatant force

$F_R=\sqrt{F_x^2+F_y^2}$

$F_R=\sqrt{150^2+86.6^2}=173.2N$

Angle

$tan\theta=\frac{-86.6}{150}\\\theta=-30°$

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