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

Question

A baby elephant is stuck in a mud hole. To help pull it out,  game keepers use a rope to apply a force   FA, as part a of the drawing  shows. By itself, however, force FA is insufficient. Therefore, two additional  forces FB and   FC are applied, as in part b of the drawing. Each of  these additional forces has the same magnitude F. The magnitude  of the resultant force acting on the elephant in part b of the drawing is k  times larger than that in part a. Find the ratio F/FA when k = 2.40.

Explanation / Answer

example for 19 degrees

It's always best to draw a force diagram, but since it's too hard here, i envision the following:

Three force arrows of the same length (equal forces) originate from a single point (the baby elephant) with F(b) and F(c) 19.0degrees apart from F(a). In my vision, F(b) and F(c) are on opposites sides of F(a) and offset each others sideways pull.

You want to find out the ratio of the total resultant force F to the original force F(a).

Since the sideways pull of F(b) and F(c) offset each other, F pulls in the same direction as F(a). The portion of F(b) and F(c) pulling in the same direction as F(a) are both simply F(a)cos(19).

You can thus right an equation for F as the sum of these three force components:

F = F(a) + F(a)cos(19) + F(a)cos(19)

If you divide both sides of the equation by F(a) and simlify you get:

F/F(a) = (1+2cos(19))

I'll let you do the actual math since I don't have a calculator handy.

Hope this helps

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