Problem

The figure shows a temperature- compensated pendulum in which lead and steel rods are arra...

The figure shows a temperature- compensated pendulum in which lead and steel rods are arranged so that the pendulum’s length is unaffected by changes in the temperature. Determine the length L of the two lead bars.

Step-by-Step Solution

Solution 1

Step #1 of 6

THINK:

The coefficients of linear expansion of the rod depend on the temperature.

Step #2 of 6

RESEARCH:

The change in the length of a rod after heating by a temperature increased an amount is given by

…… (1)

Here is the initial length of the rod and is the linear expansion coefficient.

Step #3 of 6

SIMPLIFY:

The change in the length of steel bar is

The change in the length of the lead bar is

After heating, each steel bar increases in length. So the bob will moves twice the increased distance of steel from the pivot.

So we have,

…… (2)

Step #4 of 6

SIMPLIFY:

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

Therefore the length of the lead bar is

…… (3)

Step #5 of 6

CALCULATE:

Given,

Initial length of the steel bar is

Linear expansion coefficient of steel is

Linear expansion coefficient of lead is

Step #6 of 6

Substitute the all known values in the equation (1), we get

The length of the two lead bars is

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Solutions For Problems in Chapter 17

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