Solve Simple Force Problem: Find the Ratio F/F(a)

[ian_durrant]

Homework Statement

A baby elephant is stuck in a mud hole. To help pull it out, game keepers use a rope to apply force F(a). By itself,however, force F(a) is insufficient. Therefore, two additional forces F(b) and F(c) are applied. 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 twice that in part a. Find the ratio F/F(a)

Homework Equations

It should be noted that the two end ropes are 40 degrees apart, and F(a) bisects them, creating 20 between each rope.

The Attempt at a Solution

I really don't know, i tried 2:1, but that answer didn't work, any thoughts?

 

[quantumdude]

You need to draw a vector diagram, and break the forces down into components using right triangle trigonometry. Do you know what I mean by that?

 

[ian_durrant]

ok, i drew the right trangles and got an equation like this:

cos20 = (F(a)/F) which led me to -

F(a)- .94F

and i got a ratio from F/F(a)= 1.06 (i took the inverse)

when i entered this into the computer, it said it was wrong. Did I miss something that I was supposed to do, am I supposed to multiple that by two because there are two additional ropes ?

thanks for the help

 

[quantumdude]

You're on the right track, but you're forgetting that there are 2 of these forces acting on the elephant at 20 degrees (along with Fa).