Question

A grandfather clock is controlled by a swinging brass pendulum that is 1.2 m long at a temperature of 30°C.

(a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (Round your answer to four significant figures.)

Answer 1

Here, we can use linear expansion equation which is given as

$\Delta$L = L_o$\alpha$$\Delta$ T

where L_o is original length

$\alpha$ is coefficient of linear expansion, for Brass, it is 19e-6 / ^oC

L_f - L_o = L_o$\alpha$$\Delta$ T

L_f = L_o$\alpha$$\Delta$ T + L_o

L_f = 1.2 * 19e-6 * ( 0 - 30) + 1.2

L_f = 1.199316 m

or

L_f = 1199.316 mm