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# HW13 - 13.20 The pendulum in a grandfather clock is made of...

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13.20 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 25°C? (Assume the frequency dependence on length for a simple pendulum applies.) The pendulum has a period of 00 2 Lg τπ = at 17 o C, and a period of 2 = at 25 o C. Notice that 0 τ > since 0 LL > . With every swing of the clock, the clock face will indicate that a time 0 has passed, but the actual amount of time that has passed is . Thus the clock face is “losing time” by an amount of 0 ττ ∆=− every swing. The fractional loss is given by 0 , and the length at the higher temperature is given by () ( ) 0 0 0 0 0 0 0 0 6o o 5 22 2 1 1 1 19 10 C 8C 1 7.60 10 L g L L L L L L L T L L L L T ππ α π −− + + == = = = =+ =+× = × Thus the amount of time lost in any time period 0 is ( ) 5 0 7.60 10 ∆= × . For one year, we have the following: ( )( ) 57 7.60 10 3.16 10 s 2402s 40 min × × = 13.32 A storage tank contains 21.6 kg of nitrogen ( ) 2 N at an absolute pressure of 3.65 atm. What

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HW13 - 13.20 The pendulum in a grandfather clock is made of...

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