Question

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0°. If dog A exerts a force of 270 N and dog B exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with dog A’s rope.

Answer 1

Explanations & Calculations

• A figure like the shown one fits the situation.

• The equation which is derived from the parallelogram theorem to find the resultant needs to be used here.

$\qquad\qquad \begin{aligned} \small R&=\small \sqrt{P^2+Q^2+2PQ\cos\theta} \end{aligned}$

• The angle is the including angle which is 60 degrees here.

• Once you have found the resultant, the vector angle ABC becomes fully defined.
• Using the cosine rule for this triangle, the angle $\small \theta$ which is the needed one can be found.

$\qquad\qquad \begin{aligned} \small \cos\theta&=\small \frac{AC^2+AB^2-AC^2}{2.AB.AC}\\ \small \theta &=\small cos^{-1}\Big(\frac{AC^2+AB^2-AC^2}{2.AB.AC}\Big) \end{aligned}$

• Now you can give it a try to get a numerical answer for the questions.