A circus performer\'s act involves placing a horizontal pole above an open-top c

Question

A circus performer's act involves placing a horizontal pole above an open-top circular aluminum cage filled with hungry lions. When the cage is at 0 degree C it has an inner diameter of 10.000m. The circus performer's pole, which is made of length Lst of steel, and length Lcu of copper, has length 10.003m at 0 degree C. The diagram below illustrates the situation at 0 degree C. One hot day, the temperature inside the circus tent reaches 35 degree C. At this temperature, the length of the pole matches the inner diameter of the cage, and the pole falls into the cage along with the performer. Find Lst and Lcu. The coefficients of thermal expansion for these materials are alpha A1 = 23.1 Times 10-6K-1, alpha Steel = 11.7 Times l0-6K-1, alpha cu =16.5 Times l0-6K-1. (partial answer: Original length of copper is 5.886 m.)

Explanation / Answer

diameter of cage at 35deg is = 10(1+alpha of aluminum*35)=10.008085M

LST+LCU=10.003

LST(1+alpha steel*35) + LCU(1+alpha cu *35) =10.008085

solving we get LST=4.117m , LCU=5.8855m

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