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Length of Wire To Support a Mass

I have rubber as having a negative coefficient of thermal expansion when it is under tension and that value being -43 x 10^-6/deg K. A rubberband will shrink when heated if it is under tension.

The problem has a large rubberband attached to a ceiling, a wire of aluminum of unknown cm. length attached to the hanging end of the rubberband. A mass of 100 grams is then hung from the lower end of the aluminum wire. The rubberband is stretched 10 cm. long at this point. How do I figure out the length of the aluminum wire such that the mass remains in the same position with respect to the floor of the room, no matter what the room temperature is?

Solution Preview

The positive expansion of aluminum must compensate for the contraction of the rubber.

Aluminum linear thermal expansion coefficient is bAl = 0.000023 /K (taken from ...

Solution Summary

134 words of explained calculations to work out of the positive expansion of aluminum must compensate for the contraction of the rubber to achieve this.

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