A pendulum clock uses a rock fastened to a very thin steel wire. This clock is d

Question

A pendulum clock uses a rock fastened to a very thin steel wire. This clock is designed so that one "tick" of the clock (one complete period of the pendulum) is equal to precisely 14.4 s. The clock is then heated by 10.4

Explanation / Answer

Period of this simple pendulum is given by T = 2p*sqrt(L/g) The rise in temperature changes the length of the rod, so the period changes. The change in length of the steel rod is dL = a*?T*L L1 = L + dL L1 = L(1+a*?T) where: a = linear coefficient of thermal expansion for steel ?T = difference in temperature = 11.4°C This makes a new period T1 = 2p*sqrt(L1/g) Now, since L1 > L then T1 > T and the clock will run "slow". Famous clockmaker John Harrison faced this exact problem and solved it using his "Gridiron" pendulum made of two different metals (steel, brass) that expanded at different rates so that the effective length remained constant over temperature.

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