Answer to Question #187034 in Physics for Clark Banuelos

Question

At 15 deg C, a bare wheel has a diameter of 30 cm, and the inside diameter of a steel rim is 29.930 cm. To what temperature must the rim be heated so as to slip over the wheel? For this type of steel, 𝝰 = 1.1 x 10^-5 /deg C.

Answer 1

The rim of initial diameter 29.930 cm must be heated so its diameter is less than 30 cm:

$$D_{30}=D_0(1+\alpha T),\\\space\\ T=\frac 1\alpha\bigg(\frac{D_{30}}{D_0}-1\bigg)=212°\text C.$$