A picture is suspended by two wires of equal length. Each wire makes an angle wi

Question

A picture is suspended by two wires of equal length. Each wire makes an angle with the horizontal.

a. Predict whether the tension in the wires will increase or decrease as the picture gets higher, i.e., the angle gets smaller. Explain.

b. Use the standard problem-solving strategy, find the tension T in the wire in terms of , the weight w, and any constants you need. Does your calculation support your prediction in part (a)?

c. Is it possible to hang the picture so that the wires don't sag at all, i.e., =0? Explain.

Thanks!

Explanation / Answer

Given Let the weight of the picture be w Angle made by the wires with the horizontal is The tension along x axis gets compensated and there will be tension only along y axis a) As the picture is raised, the angle becomes smaller . Now, the weight is acting down wards and the tension will be more in the wires to compensate that weight b)Net force along y axis is 2T sin = w T = w /2sin As the angle gets smaller , the tension gets inceased. Because the tension is inversely prooportional to the angle made the wires with the horizontal The calculation supports our prediction c)No, it is not possible to hang the picture without th ewires sagging.If = 0, the tension in the wires get infinity and the wires cannot withstand the weight of the picture

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