Concept explainers
(a)
Find the energy of the pendulum.
(a)
Answer to Problem 77P
The energy of the pendulum is
Explanation of Solution
Write the equation for total mechanical energy of a pendulum.
Here,
Write the equation for angular frequency of the
Here,
Conclusion:
Substitute equation (II) in (I).
Substitute
Therefore, the energy of the pendulum is
(b)
Find the percentage of the pendulum’s energy lost during one cycle.
(b)
Answer to Problem 77P
The percentage of the pendulum’s energy lost during one cycle is
Explanation of Solution
Write the equation for time period of the pendulum.
Here,
Write the equation for potential energy of an object.
Here,
The loss of oscillation time period of cycle for 1 week is.
The percentage of pendulum’s energy loss for 1 week is.
Here,
Conclusion:
Substitute equation (IV) in (VI).
Substitute the equation (III), (V) and (VIII) in equation (VII).
Substitute
Therefore, the percentage of the pendulum’s energy lost during one cycle is
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