In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on a

Question

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite of the three pulls. Alex pulls with force F with rightarrow A of magnitude 220 N, and Charles pulls with force F with rightarrow C of magnitude 179 N. Note that the direction of F with rightarrow C is not given. What is the magnitude of Betty's force F with rightarrow B if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium?

Explanation / Answer

here

Alex is 131º from +x axis, and Betty is 270º.

To balance horizontally,

220N*cos131º + 179N*cos = 0

cos = 0.8063

This has two solutions (as noted above) --

= ± 36.26º

(a)

220 * sin131 + 179 * sin36.26 + F * sin270 = 0

F = 271.9 N

(b)

220 * sin131 + 179 * sin-36.26 + F * sin270 = 0

F = 60.16 N

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