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(5.) (1) A pendulum clock has a rod with a period of 2 s at 20 °C. If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)

(5.) (1) A pendulum clock has a rod with a period of 2 s at 20 °C. If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)

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de dt = (0.25 m)(0.17)(2π) cos( = -0.123 m/s V = L cos (+) EXAMPLE 15.8: A uniform rod of mass m and length L is freely pivoted at one end. (a) What is the period of its oscilla- tion? (b) What is the length of a simple pendulum with the same period? Solution: (a) The moment of inertia of a rod about one end is I = mL² (Eq. 11.18). The center of mass of a uniform rod is at its center, so d = L/2 in Eq. 15.17. The period is 2L mL2/3 = 27 mgL/2 3g (b) Comparing Eq. 15.17 with T = 27 VL/g for a simple pendu- lum, we see that the period of a physical pendulum is the same as that of an "equivalent" simple pendulum of length T = 2π For the uniform rod Leq Leq md = - mL²/3 (mL/2) 2L 3
Transcribed Image Text:de dt = (0.25 m)(0.17)(2π) cos( = -0.123 m/s V = L cos (+) EXAMPLE 15.8: A uniform rod of mass m and length L is freely pivoted at one end. (a) What is the period of its oscilla- tion? (b) What is the length of a simple pendulum with the same period? Solution: (a) The moment of inertia of a rod about one end is I = mL² (Eq. 11.18). The center of mass of a uniform rod is at its center, so d = L/2 in Eq. 15.17. The period is 2L mL2/3 = 27 mgL/2 3g (b) Comparing Eq. 15.17 with T = 27 VL/g for a simple pendu- lum, we see that the period of a physical pendulum is the same as that of an "equivalent" simple pendulum of length T = 2π For the uniform rod Leq Leq md = - mL²/3 (mL/2) 2L 3
5.)(1) A pendulum clock has a rod with a period of 2 s at 20 °C. If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)
Transcribed Image Text:5.)(1) A pendulum clock has a rod with a period of 2 s at 20 °C. If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)
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