Chapter 10, Problem 12P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A grandfather clock is controlled by a swinging brass pendulum that is 1.3 m long at a temperature of 20.0°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (b) If a pendulum’s period is given by T  = 2 π L / g , where L is its length, does the change in length of the rod cause the clock to run fast or slow?

(a)

To determine
The length of pendulum (L) at 0.0οC .

Explanation

Given Info: The length of pendulum at 20Î¿C . ( L0 ) is 1.3 m. The temperature changes from T1=20.0Î¿C to T2=0.0Î¿C Â  Co-efficient of expansion of brass ( Î± ) is 19Ã—10âˆ’6/Î¿C

Formula to calculate the change in length is,

Î”L=Î±L0Î”T Â Â Â Â Â  (I)

• Î”T is the change in temperature.

The change in temperature is,

Î”T=T2âˆ’T1

The change in length is,

Î”L=Lâˆ’L0

Substitute Lâˆ’L0 for Î”L and T2âˆ’T1 for Î”T in Equation (I) and re-arrange

(b)

To determine
Whether the clock runs fast or slow.

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