Solving the Stuck Ring Problem Using Expansion Coefficients

[skwerl]

A brass ring of diameter 10.00 cm at 19.5C is heated and slipped over an aluminum rod of diamter 10.01 cm at 19.5C. Assume the average coefficients of linear expansion are constant.

a) To what temperature must this combination be cooled to separate them? is this possible?
b) If the aluminum rod were 10.03 cm in diameter, what would be the required temperature? Is this possible?

B(brass) = 19x10^-6
B(alum) = 24x10^-6

Well...let's see... first I thought of heating the brass until it was wide enough to slip over the tube, and then I tried to set up some kind of relationship and failed miserably.

oh and by the way I'm new! hi guys!

 

[Doc Al]

Well...let's see... first I thought of heating the brass until it was wide enough to slip over the tube, and then I tried to set up some kind of relationship and failed miserably.

Welcome to Physics Forums!

When the temperature is reduced, both metals will contract. The question is will they contract enough to separate?

The length is given by: L = L₀(1 + α ΔT). Set it up and solve for the temperature that will make both metals the same diameter.

Hints: You know the "unstressed" diameter of both metals at 19.5°C, so start there. Also, what is the maximum possible ΔT?

 

[skwerl]

neat. so much more elegant than what I thought of

thanks!