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 FA→ of magnitude 212 N, and Charles pulls with force FC→ of magnitude 177 N. Note that the direction of FC→ is not given. What is the magnitude of Betty's force FB→

University Physics Volume 2
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Chapter1: Temperature And Heat
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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 FA→ of magnitude 212 N, and Charles pulls with force FC→ of magnitude 177 N. Note that the direction of FC→ is not given. What is the magnitude of Betty's force FB→ if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium?

Alex
Charles
140°
Betty
Transcribed Image Text:Alex Charles 140° Betty
Expert Solution
Step 1

From the diagram,

Alex's angle from the positive x-axis, θA = 270 - 140 θA = 130°θB = -90°Force by Alex, FA = 212 NForce by Charles, FC = 177 NForce by Betty, FB = ?

At equilibrium, the total Force is zero.

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