The concepts that play a role in this problem. As an aid in working this problem

Question

The concepts that play a role in this problem. As an aid in working this problem, consult Concept Simulation 1.1. Two forces are applied to a tree stump to pull it out of the ground. Force F_A has a magnitude of 1610 newtons (N) and points 34.0 degree south of east, while force F_B has a magnitude of 2130 N and points due south. Using the component method, find the (a) magnitude and (b) direction of the resultant force F_A + F_B that is applied to the stump. Specify the direction as a positive angle with respect to due east.

Explanation / Answer

East direction is supposed to be along X axis and South along Y axis. Force of 1610N is resolved along East and South. It's component along East = 1610 cos340 = 1610 x 0.829 = 1334.69N. component along South = 1610 sin340 = 1610 x 0.559 = 900N. But there is already a force of 2130N along South, so total force along South = 2130 + 900 = 3030 N. So now using Pythagoras theorem, resultant of these two forces = 3311N and direction from East is tan theta = 3030/1334.69 = 2.27, so angle = 66.30

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