Solution Found!
Temperature Change in a Clock. A pendulum clock is
Chapter 17, Problem 126CP(choose chapter or problem)
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 reserve? 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 10.0°C (c) How many seconds per day will the clock gain or lose at 10.0°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?
Questions & Answers
QUESTION:
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 reserve? 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 10.0°C (c) How many seconds per day will the clock gain or lose at 10.0°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?
ANSWER:Solution 126CP 1 day = 24 × 60 × 60 = 86,400 s 5 01 a)coefficient of linear expansion of steel, = 1.2 × 10 C a) We have equation I T = mgd In hot weather, the moment of inertia I and the length d will both increase by the same factor, and so the period will be