Concept explainers
The pendulum in a grandfather clock is made of brass and keeps perfect time at 17°C. How much time is gained or lost in a year if the clock is kept at 29°C? (Assume the frequency dependence on length for a simple pendulum applies.) [Hint:See Chapter 8)
The time lost or gained in a year if the pendulum clock is kept at the given higher temperature
Answer to Problem 18P
Solution:
The pendulum clock will lose approximately 60 minutes (or 1 hour)in a year.
Explanation of Solution
Given:
Initial temperature,
Final temperature,
The pendulum is made of brass
Formula used:
i) The time period of a pendulum clock is given by,
, where l0 is the length of the pendulum
ii) The relation between change in length of a substance and change in temperature is given by,
, where ΔT is the change in temperature andΔ is the coefficient of linear expansion of a material.
Calculation:
The time period of a pendulum clock is given by,
, where l0 is the length of the pendulum
Since the time period depends on the length of the pendulum, a change in this length because of change in temperature will have an effect on the time period also
The relation between change in length of a substance and change in temperature is given by,
, where ΔT is the change in temperature andΔ is the coefficient of linear expansion of a material.
If Δt is the time lost or gained, we have
=
=
=
or
or
For brass,
Based on the given data,
Therefore,
Chapter 13 Solutions
Physics: Principles with Applications
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