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The homogeneous wire ABC is bent into a semicircular arc and a straight section as shown and is...

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The homogeneous wire ABC is bent into a semicircular arc and a straight section as shown and is attached to a hingeat A. Determine the value of θ for which the wire is in equilibrium for the indicated position

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Answer #1

Draw the schematic diagram of homogeneous wire dividing the wire into two segments.

Picture 1

Determine the position of centroid of segment 1 which is a straight line from A.

Here, is length of the wire in segment 1 and is the angle of inclination of the wire with the horizontal.

Determine the position of centroid of segment 2 which is a semicircular arc from A.

Determine the angle of inclination by using centroid formula at A.

Substitute for , for , for , and for .

Therefore, the angle of inclination of the straight wire with the horizontal is .

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