Posted by **Jimmy Turner** on Sunday, May 27, 2012 at 5:40pm.

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 cos = 25

- Physics -
**Elena**, Sunday, May 27, 2012 at 5:59pm
As the forces FB and FC are equal the horizontal component of force is given as FB = FC = F•cos θ,

θ =22º

The net force applied on the elephant is

Fnet = FA + 2 F•cos θ ........ (1) ( there are two forces on either side of FA)

Given that Fnet is k times FA

Fnet = k• FA where k = 2.32•FA

Fnet = 2.32• Fa .............. (2)

Plug in (2) in (1)

2.32 •FA = FA + 2• F• cos θ

2.32• FA - FA = 2• F•cos θ

(2.32 - 1) • FA = 2 F cos θ

1.32• FA= 2• F• cos θ

Ratio

F / FA = 1.32/( 2• cos θ)=

=1.32/2•cos22º = 0.71

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