A commonly used method of fastening one part to another part is called \"shrink

Question

A commonly used method of fastening one part to another part is called "shrink fitting." A steel rod has a diameter of 2.0022 cm, and a flat plate contains a hole whose diameter is 2.0000 cm.  The rod is cooled so that it just fits into the hole.  When the rod warms up, the enormous thermal stress exerted by the plate holds the rod securely to the plate.  By how many Celsius degrees should the rod be cooled? (See Table 12.1 for appropriate constants.)
     C

A commonly used method of fastening one part to another part is called "shrink fitting." A steel rod has a diameter of 2.0022 cm, and a flat plate contains a hole whose diameter is 2.0000 cm. The rod is cooled so that it just fits into the hole. When the rod warms up, the enormous thermal stress exerted by the plate holds the rod securely to the plate. By how many Celsius degrees should the rod be cooled? (See Table 12.1 for appropriate constants.)

Explanation / Answer

The area must be reduced from ?*ri^2 to ?*rf^2

which is ?*((1.0011x10^-2m)^2 - (1.00x10^-2m)^2) = 6.91x10^-7m^2

Now we have that ?A = 2*?*A*?T

so ?T = ?A/(2*?*A) = 6.91x10^-7/(2*1.2x10^-5*?*ri^2) = 6.91x10^-7/(2*1.2x10^-5*?*(1.0011x10^-2...

= 91.44 oC

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