A man stands on a weighing machine placed on a horizontal platfor… - Vidyadip

Question

A man stands on a weighing machine placed on a horizontal platform. The machine reads $50kg$. By means of a suitable mechanism the platform is made to execute harmonic vibrations up and down with a frequency of $2$ vibrations per second. What will be the effect on the reading of the weighing machine? The amplitude of vibrations of platform is 5cm. Take $g = 10ms^{-2}$?

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Answer

Here, $m = 50kg, v = 2s^{-1} a = 5cm = 0.05m$ Max. acceleration$\text{a}_{\text{max}}=\omega^2\text{A}=(2\pi\text{v})^2\text{A}=4\pi^2\text{v}^2\text{A}$
$=4\times\Big(\frac{2}{7}\Big)^2\times(2)^2\times0.05$
$=7.9\text{ms}^{-2}$
$\therefore$ Maximum force felt by the man $= m(g + a_{max}) = 50(10 + 7.9) = 895.0N = 89.5kg f$
Minimum force felt by the man = $m(g - a_{max}) = 50(10 - 7.9) = 105.0 = 10.5kg\ f$
Hence, the reading of the weighing machine varies between 10.5kg f and 89.5kg f.

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