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A uniform wire of length L and weight W is fixed at its upper end to a point on the roof, and a load of weight W1 is hung from its lower end. If the wire has cross-sectional area s, what is the stress in the wire at a point located 3L/4 above the lower end?

1. W1/s
2. (W1 + W/4)/s
3. (W1 + 3W/4)/s
4. (W1 + W)/s

Correct answer: (W1 + 3W/4)/s

Solution

The stress at a cross-section equals the total weight hanging below it divided by area. Below a point 3L/4 above the lower end there is length 3L/4 of wire (weight 3W/4) plus the load W1. So stress = (W1 + 3W/4)/s.

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