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6 June, 13:10

A grandfather clock is controlled by a swinging brass pendulum that is 1.2 m long at a temperature of 27°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (Round your answer to four significant figures.) mm

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  1. 6 June, 13:11
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    L2 = 1.1994 m

    the length of the pendulum rod when the temperature drops to 0.0°C is 1.1994 m

    Explanation:

    Given;

    Initial length L1 = 1.2m

    Initial temperature T1 = 27°C

    Final temperature T2 = 0.0°C

    Linear expansion coefficient of brass x = 1.9 * 10^-5 / °C

    The change i length ∆L;

    ∆L = L2 - L1

    L2 = L1 + ∆L ... 1

    ∆L = xL1 (∆T)

    ∆L = xL1 (T2 - T1) ... 2

    Substituting the given values into equation 2;

    ∆L = 1.9 * 10^-5 / °C * 1.2m * (0 - 27)

    ∆L = 1.9 * 10^-5 / °C * 1.2m * ( - 27)

    ∆L = - 6.156 * 10^-4 m

    From equation 1;

    L2 = L1 + ∆L

    Substituting the values;

    L2 = 1.2 m + ( - 6.156 * 10^-4 m)

    L2 = 1.2 m - 6.156 * 10^-4 m

    L2 = 1.1993844 m

    L2 = 1.1994 m

    the length of the pendulum rod when the temperature drops to 0.0°C is 1.1994 m
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