THERMODYNAMICS SUB-MENU ThermoDynamics Sub-menu Problem #0002ChaptersChapters


201.


Problem 22.41 (RHK)


A pendulum clock with a pendulum made of brass is designed to keep accurate time at . We have to estimate the error in seconds per hour when the clock operates at .


Solution:           Click For PDF Version

 We will first find the length of the pendulum for it to have a period of 1 s when it operates at . The period of the pendulum is related to its length, l, and the acceleration due to gravity, g, as

For ,


Change in length of the brass second-pendulum when it operates at , will be

The length of the pendulum of the clock at will therefore be



This clock will show 1-second lapse after each period of the pendulum. The period of oscillation of the pendulum at will be

That is when time lapse is 0.9998106 s the clock shows that 1 s has lapsed.

Therefore, error in 1 s is

Error in 1 hour will be