Acommonly used method of fastening one part to another part is called "shrink fitting." a steel rod has a diameter of 2.0024 cm, and a flat plate contains a hole whose diameter is 2. 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?

The steel rod should be cooled by 99.88°C

Explanation:

To solve this exercise we require the thermodynamic concept of thermal expansion.

Here it is necessary to have the coefficient of thermal expansion for steel, since the formula to calculate is:

Where

ΔL represents the change in length,

is the initial length,

α is the coefficient of thermal expansion

ΔT the change in temperature.

α of the steel is

The longitudinal change of our material is of

Replacing,

Solving to ,

Therefore the steel rod should be cooled by 99.88°C

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