Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-Two boats are pulling a disabled vessel toward the landing dock with forces of $940 \mathrm { lb }$ and $930 \mathrm { lb }$. The angle between the forces is $25.7 ^ { \circ }$. Find the direction and magnitude of the equilibrant.
A) $182 \mathrm { lb }$ at an angle of $167.2 ^ { \circ }$ with the $940 - \mathrm { lb }$ force
B) $1823 \mathrm { lb }$ at an angle of $12.8 ^ { \circ }$ with the $940 - \mathrm { lb }$ force
C) $1823 \mathrm { lb }$ at an angle of $77.2 ^ { \circ }$ with the $930 - \mathrm { lb }$ force
D) $1823 \mathrm { lb }$ at an angle of $167.2 ^ { \circ }$ with the $940 - \mathrm { lb }$ force

Question

Quizplus · Accepted Answer

The magnitude of the resultant force is:$$R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos\theta}$$$$R = \sqrt{940^2 + 930^2 + 2(940)(930)\cos25.7^\circ}$$$$R = 1823 \mathrm { lb}$$The direction of the resultant force is:$$\theta = \tan^{-1}\left(\frac{F_2\sin\theta}{F_1 + F_2\cos\theta}\right)$$$$\theta = \tan^{-1}\left(\frac{930\sin25.7^\circ}{940 + 930\cos25.7^\circ}\right)$$$$\theta = 167.2^\circ$$Therefore, the equilibrant is $1823 \mathrm { lb }$ at an angle of $167.2 ^ { \circ }$ with the $940 - \mathrm { lb }$ force.

Use the Parallelogram Rule to Find the Magnitude of the Resultant