...A baby elephant is stuck in a mud hole. To help pull it out, game keepers use

Question

...A baby elephant is stuck in a mud hole. To help pull it out, game keepers use a rope to apply force A, as part (a) of the drawing shows. By itself, however, force A is insufficient. Therefore, two additional forces B and C are applied, as in part (b) of the drawing. Each of these additional forces has the same magnitude F and is oriented at ? = 19.0° away from A. The magnitude of the resultant force acting on the elephant in part (b) of the drawing is eight times that in part a. Find the ratio F / FA?

Explanation / Answer

Component of FA perpendicular to FA = 0 because component of any vector perpendicular to the vector = 0.
If we take components of FB and FC perpendicular to FA, then they cancel each other because FA and FB are on opposite sides of FA and make same angle with FA.

Therefore, resultant force = sum of components of the three forces along FA.
Or resultant force = FA + F cos? + F cos?
= FA + 2F cos?
= FA + 2F cos 20.5°
It is given that resultant force = 8 FA
Therefore
FA + 2F cos 20.5° = 8 FA
Or 2F cos 20.5°= 7 FA
O F/FA = 7/(2 cos 20.5°)
= 3.5/cos 20.5°
= 3.5/0.94
= 3.72

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