Applications of Vectors

Question

Two vessels are pulling a broken-down ship toward a boathouse with forces of 750 lb and 630 lb. The angle between the forces is 34.5°

1.  The magnitude of the equilibrant force would be _____ pounds. Round your answer to the nearest thousandth of a pound.

Answer 1

Draw the force vector parallelogram with 34.5° being the angle at the attachment of the forces to the ship. The triangle that includes the two force vectors and has a third side that is the resultant vector (the vector sum of the forces) requires the other angle of the parallelogram 1/2 (360-2(34.5)) = 180 - 34.5 = 145.5 = θ

Now you can use cosine law to find the resultant F_Tot² = F₁² + F₂² - F₁F₂cos(θ)

The problem mentions the equilibrant, which doesn't exist unless the system is in mechanical equilibrium (going a constant speed). In equilibrium the equilibrant is of the same magnitude as the resultant and in the opposite direction.