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A thin string is held at one end andoscillates vertically so that,y = (x =0, t) = 8 sin (4t) (cm) Neglect the gravitational force. The string'slinearDiass density is 0.2 kg/m and its tension is 1 N. The string passes through a bath filled with 1 kg water, Due to friction heat is transferted to the bath. The heat transfer efficiency is 50%. Calculate how much time passes before the temperature of the bath rises by one degree kelvin. |
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Answer» <P> Solution :Comparing the given equation with equation of a travelling wave, `kg//m` The AVERAGE power over a period is, `P = 1/2 (rho S) omega^2 A^2v`Substituting the values, we have `P = 1/2 (0.2) (4)^2 (8 xx 10^(-2))^2 (2.236) = 2.29 xx 10^(-2)J//s` Now let it take t second to raise the temperature of 1 kg water by one degree KELVIN. Then `Pt = ms Deltat` Here, s = specific heat of water `= 4.2 xx 10^3 J//kg -K` `:. t = (msDeltat)/(P xx 1/2) = ((1) (4.2 xx 10^3) (1))/(1.145 xx 10^(-2)) ~~ 4.2` day |
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