Temperature Change in a Clock. A pendulum clock is designed to tick off one second on each side-to-side swing of the pendulum (two ticks per complete period).
(a) Will a pendulum clock gain time in hot weather and lose it in cold, or the reverse? Explain your reasoning.
(b) A particular pendulum clock keeps correct time at 20.0°C. The pendulum shaft is steel, and its mass can be ignored compared with that of the bob. What is the fractional change in the length of the shaft when it is cooled to to.0°C?
(c) How many seconds per day will the clock gain or lose at to.0°C?
(d) How closely must the temperature be controlled if the clock is not to gain or lose more than 1.00 s a day? Does the answer depend on the period of the pendulum?