# Physics 4B

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To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.873 cm in diameter is to be placed in a hole 1.871 cm in diameter in a metal at 20°C. To what temperature must the rivet be cooled if it is to fit in the hole?

• Physics 4B - ,

First, look up the coefficient of thermal expansion of steel. Call it "a". Let the change in temperature necessary to shrink the rivet to fit the hole be "delta T". It will be a negative number in this case. It depends up the type of steel you have: structural (carbon) steel or stainless steel. They should have told you which it is. A reasonable number to use is
a = 13*10^-6 (deg C)^-1

D2 = final rivet diameter
D1 = initial rivet diameter

Solve the equation
D2 - D1 = -0.002 = 1.873*a*(delta T)
delta T = -0.00107/a

and add that to the initial temperature. Since deelta T is negative, you will end up with a colder temperature