(Solution) - A uniform cable of weight w hangs vertically -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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A uniform cable of weight w hangs vertically downward, supported by an upward force of magnitude w at its top end. What is the tension in the cable
(a) At its top end;
(b) At its bottom end;
(c) At its middle? Your answer to each part must include a free body diagram. (Hint: For each question c bourse the body to analyze to be a section of the cable or a point along the cable)
(d) Graph the tension in the rope versus the distance from its top end.