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

Question

n a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure. The tire remains stationary in spite of the three pulls. Alex pulls with force of magnitude 207 N, and Charles pulls with force of magnitude 150 N. Note that the direction of Charles' force is not given. What is the magnitude of Betty's force?

Explanation / Answer

From sine rule; 150/sin137 = 207/sin(theta) = F/sin(360-theta-137) => 219.94 = 207/sin(theta) = F/sin(223-theta) => theta = sin^-1(207/219.94) = 70.248 degrees F = 219.94* sin(223 - 70.248) = 100.697 N

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