Question

he pendulum shaft of a clock is made of brass. What is the fractional change in length of the shaft when it is cooled from 19.50 to 5.0?

Answer 1

Answer:

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Explanation:

There are several types of brass, with thermal expansion coefficients ranging from 18.7 (red brass) to 21.2 (naval brass), in units of 10^-6 meter/meter per degree C. So the fractional change in length is a shortening by 2.711 to 3.074 X 10^-4 m/m. or, if the shaft was one meter in length, it would be shorter by 0.27 to 0.31 millimeters (a little over a hundreth of an inch).

Answer 2

Given: The pendulum shaft of a clock is made of brass. It is cooled from 19.5°C to 5° C

To find: Fractional change in the length of the shaft

Explanation: Let the original length of pendulum shift of the clock be l1 and the new length after cooling be l2.

Let the linear coefficient of thermal expansion of brass be a.

$a = 19 \times {10}^{ - 6}$

Temperature change(t)

= New temperature- Old temperature

= 19.5 ° C - 5° C

= 14.5° C

Fractional change= l2 - l1 / l1

The formula for change in length when the shaft is cooled is:

$l2 = l1 + l1 \times a \times t$

$l2 - l1 = l1 \times a \times t$

$\frac{l2 - l1}{l1} = a \times t$

$\frac{l2 - l1}{l1} = 19 \times {10}^{ - 6} \times 14.5$

$\frac{l2 - l1}{l1} = 275.5 \times {10}^{ - 6}$

Therefore, the fractional change in length of the shaft when it is cooled from 19.5° C to 5° C is $275.5 \times {10}^{ - 6}$.