Question

Two rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lb and 960 lb. The angle between these forces is 24.5°. Find the direction and magnitude of the equilibrant.

Accepted Answer

Identify the two forces acting on the motorboat: $$F_1 = 840$ lb and F_2$ = 960 lb$$, with an angle $$	heta = 24.5^\circ$$ between them. Calculate the resultant force $$\vec{R} by $$using the Law of Cosines to find its magnitude: $$R = \sqrt{F_1$^2 + F_2$^2 + 2 F_1$ F_2$ \cos(	heta)}. $$Find the direction of the resultant force relative to the first force $$F_1$$ using the Law of Sines or the formula: $$\alpha = \arctan\left(\frac{F_2$ \sin(	heta)}{F_1$ + F_2$ \cos(	heta)}ight)$$, where $$\alpha is $$the angle between $$F_1$$ and $$\vec{R}. $$Understand that the equilibrant force $$\vec{E} is $$equal in magnitude but opposite in direction to the resultant force $$\vec{R}$$, so its magnitude is the same as $$R$$ and its direction is $$\alpha + 180^\circ (or $$directly opposite to $$\vec{R}). $$Summarize the final answers: the magnitude of the equilibrant is $$R$$, and its direction is $$\alpha + 180^\circ$$ relative to the direction of $$F_1.$$

Two rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lb and 960 lb. The angle between these forces is 24.5°. Find the direction and magnitude of the equilibrant.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Vector Addition of Forces

Law of Cosines

Equilibrant Force