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1 August, 16:10

A Foucault pendulum consists of a brass sphere with a diameter of 32.0 cm suspended from a steel cable 10.0 m long (both measurements made at 20.0∘C). Due to a design oversight, the swinging sphere clears the floor by a distance of only 3.00 mm when the temperature is 20.0∘C. c. at what temperature will the sphere begin to brush the floor?

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  1. 1 August, 16:39
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    T = 44.35 °C

    Explanation:

    d = 32cm

    R = 16 cm

    Lsteel = 10m

    T1 = 20° C

    Space = 0.3cm

    The space between the sphere and the floor is represented by δL (total) after the temperature increases.

    As the temperature increases, both will expand.

    So,

    0.3 x 10^ (-2) = δL (steel) + δR (brass)

    = {L (o) x α (steel) x δT} + {R (o) x {α (brass) x δT}

    = {10 x 1.2 x 10^ (-5) x (T-20) } + {0.16 x 2 x 10^ (-5) x (T-20) }

    = 12.32 x 10^ (-5) x (T-20)

    Therefore (T-20) = (0.3 x 10^ (-2)) / {12.32 x 10^ (-5) }

    T = 20 + 24. 35 = 44.35 °C
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