Problem

In order to create a tight fit between two metal parts, machinists sometimes make the inte...

In order to create a tight fit between two metal parts, machinists sometimes make the interior part larger than the hole into which it will fit and then either cool the interior part or heat the exterior part until they fit together. Suppose an aluminum rod with diameter D 1 (at 2.0 ∙101 °C) is to be fit into a hole in a brass plate that has a diameter D 2 = 10.000 mm (at 2.0 ∙101 °C). The machinists can cool the rod to 77.0 K by immersing it in liquid nitrogen. What is the largest possible diameter that the rod can have at 2.0∙101 °C and just fit in to the hole if the rod is cooled to 77.0 K and the brass plate is left at 2.0-101 °C? The linear expansion coefficients for aluminum and brass are 22∙10-6 °C-1 and 19∙10-6 °C-1 , respectively.

Step-by-Step Solution

Solution 1

THINK:

Consider the change in the diameter of the rod as linear expansion.

Linear expansion coefficient of the aluminum is

Linear expansion coefficient of brass is

RESEARCH:

The new length of diameter of a rod after cooling as change in the temperature is given by

…… (1)

Here is the initial length of the rod, is the linear expansion coefficient and is the change in the temperature.

SIMPLIFY:

From the equation (1),

The initial length of the diameter of the rod is …… (2)

CALCULATE:

Given,

New diameter of the rod at temperature is

The initial temperature is

After cooling, the final temperature is

The change in the temperature is

Substitute the all known values in the equation (2), we get

The possible initial length of the rod is

Add your Solution

Textbook Solutions and Answers Search

Solutions For Problems in Chapter 17

ADVERTISEMENT

Free Homework Help App

Download From Google Play

Scan Your Homework
to Get Instant Free Answers

Need Online Homework Help?

Ask a Question

Get Answers For Free
Most questions answered within 3 hours.

ADVERTISEMENT

Recent Solutions