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A perosn normally weighting 50kg stands on a massless platform which oscillates up and down harmonically at a frequency of `2.0s^(-1)` and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time. (a) Will there be any in weight of body , during the oscillation? (b) If answer to part (a) is yes, what will be the maximum and minimum readin in the machine and at which position? |
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Answer» (a) Yes, We know that when a platform on which a perosn of mass m is standing, is accelerating upwards with acceleration a, then the effective weight of the person becomes`=m(g+a)`. If the platform is accelerating downwards with acceleration a, then effective weight of persono on platform `=m(g-a)` . During oscillation of a platform, a perosn standing on it, will be accelerated upwards and downwards with time. Due to it, the weight of a person on platform changes during the oscillation. (b) Max. acceleration of platfor, `a_(max.)=omega^(2)r=4pi^(2)v^(2)r=4xx(3.14)^(2)xx2^(2)xx(5xx10^(-2))=7.89m//s^(2)` Maximum reading in machine while moving upwards `=m(g+a)=50(9.8+7.89)=884.5N` Minimum readin in machine while moving downwards `=m(g-a)50(9.8-7.89)=95.5N` |
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