Question

The 1.5-m-long brass pendulum of a grandfather clock was manufactured on a day when the temperature was 27°C. The coefficient of linear expansion for brass is 19 ? 10?6/°C. (a) What would the length be if the temperature were to increase to 31.0°C? (Give your answer to at least 4 decimal places.) m (b) Will the clock gain or lose time due to the change in length of the pendulum? gain time lose time neither gain nor lose time

Answer 1

Given :

l = 1.5 m

T1 = 27 C

T2 = 31 C

= 19 x 10^-6 /C

a)

strain = T

= l / l =  T

(l2 - l1) / l1 = 19 x 10^-6 x (31 - 27)

(l2 - 1.5) / 1.5 = 19 x 10^-6 x 4

l2 - 1.5 = 0.000114

l2 = 1.500114 m

b)

T = 2pi*sqrt(L/g)

T = 2pi*sqrt(1.500114/9.81)

T = 2.4570 sec

Initial time,

T = 2pi*sqrt(L/g)

T = 2pi*sqrt(1.5/9.81)

T = 2.45692 sec

change in time =  2.4570 sec -  2.45692 sec = 7.9999 x 10^-5 sec