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Question:

Physics Challenge Problem?

You need to make a 1.00-m-long bar that expands with temps in the same way as a 1.00-m-long bar of copper would. Your bar must be made from a bar of iron and a bar of aluminum attached end to end. How long should each of them be?

Answer:

It depends on the style of riding you do, how often you do it and do you properly maintain your air pressure. Most motorcycle tires will last 8-12k depending on the user. There is no right answer. Check your pressure daily to ensure proper inflation. That affects your wear. Keep it maintained and you don't replace as often. Do you do a lot of twistys? Likely you will need to replace sooner. Call the manufacturer of the tire and cruise forums on your particular bike.
For the copper bar of initial length L: ΔL L * α_copper * ΔT For the compound bar ΔL ΔL_iron + ΔL_alu x * α_iron * ΔT + (L -x) * α_alu * ΔT So the length of the iron part should be x * ( α_iron - α_alu) * ΔT - L* α_alu * ΔT L * α_copper * ΔT x L * ( α_copper + α_alu) / ( α_iron - α_alu) So look up the linear expansion coefficients of iron, aluminium an copper to calculate x, the length of the iron part. L - x then remains for the aluminium.
When you get down to the wear indicators or you start seeing the threads or steel belting.

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