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?

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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