What Temperature Allows a Brass Plug to Fit into an Iron Ring?

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SUMMARY

The discussion focuses on determining the temperature at which a brass plug can fit into an iron ring. At room temperature (20°C), the brass plug has a diameter of 8.764 cm, while the iron ring has an inside diameter of 8.754 cm. The coefficients of linear expansion for brass and iron are 56x10^-6 and 35x10^-6, respectively. By equating the expanded radii of both materials and solving for the change in temperature (Δt), the required temperature for fitting can be calculated.

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Homework Statement


A brass plug is to be placed in a ring made of iron. At room temperature (20°C), the diameter of the plug is 8.764 cm and that of the inside of the ring is 8.754 cm. They must both be brought to what common temperature in order to fit?


Homework Equations


Change in V=B*V0*Change in T
B for brass = 56x10^-6
B for Iron = 35 x 10^-6


The Attempt at a Solution


I had no idea how to start i notice that the change in the coefficient of expansion is going to change the items dimensions but i honestly don't know where to begin, do i combine the 2 separate formulas? how would i solve for the temperture?
 
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Here you need not consider the volume expansion. Brass plug will pass through iron ring if their radii are the same.
Rb = Rb0( 1 + αb*Δt)
Ri = Ri0( 1 + αi*Δt)
where α is the coefficient of linear expansion which is equal to B/3.
Equate Rb and Ri and solve for Δt
 

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