   Chapter 10, Problem 12P

Chapter
Section
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 20οC . ( L0 ) is 1.3 m. The temperature changes from T1=20.0οC to T2=0.0οC   Co-efficient of expansion of brass ( α ) is 19×106/οC

Formula to calculate the change in length is,

ΔL=αL0ΔT       (I)

• ΔT is the change in temperature.

The change in temperature is,

ΔT=T2T1

The change in length is,

ΔL=LL0

Substitute LL0 for ΔL and T2T1 for ΔT in Equation (I) and re-arrange

(b)

To determine
Whether the clock runs fast or slow.

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