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Consider a bimetallic strip consisting of a 0.50-mm- thick brass upper strip welded to a 0...

Consider a bimetallic strip consisting of a 0.50-mm- thick brass upper strip welded to a 0.50-mm-thick steel lower strip.When the temperature of the bimetallic strip is increased by 20. K, the unattached tip deflects by 3.0 mm from its original straight position, as shown in the figure. What is the length of the strip at its original position?

Step-by-Step Solution

Solution 1
Step #1 of 11

THINK:

The linear expansion coefficient of steel is

The linear expansion coefficient of brass is

So the brass will become larger in length.

Step #2 of 11

SKETCH:

The figure is as below:

Step #3 of 11

RESEARCH:

From the diagram,

…… (1)

Relation between arc length, angle and radius is given by, so

…… (2)

…… (3)

Step #4 of 11

The new lengths of the strips after increasing temperature are given by

The increased length of the each strip is

…… (4)

…… (5)

Here the initial lengths of the both are same

Step #5 of 11

SIMPLIFY:

From equation (2), (3)

…… (6)

Step #6 of 11

Substitute the equations (4) and (5) in the equation (6), we get

…… (7)

Here

Step #7 of 11

From the equation (1),

Now consider the difference,

Step #8 of 11

From the equation (2) and (3), we get

Therefore,

…… (8)

Step #9 of 11

From the equation (7) and equation (8), we get

…… (9)

Step #10 of 11

CALCULATE:

Given,

Thickness of the each strip is

Temperature increased is

The unattached tip deflects by

Step #11 of 11

Calculate the value of:

By substituting all known values in the equation (9), we get

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