Aman stands on a weighing machine placed on a horizontal platform… - Vidyadip

Question

Aman 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 two 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. $m = 50kg. v = 2s^{-1} A = 5cm = 0.05m$ Maximum acceleration$\text{a}_\text{max}=\omega^2\text{A}$
$=(2\pi\text{v}^2)\text{A}=4\pi^2\text{v}^2\text{A}$
$=4\times\Big(\frac{22}{7}\Big)^2\times(2)^2\times0.05$
$=7.9\text{cm}^{-2}$
$\therefore$ Maximum force felt by the man $=\text{m}(\text{g}+\text{a}_\text{max})$
$=50(10+7.9)$
$=895.0\text{N}$
$=89.5\text{kgf}$
Minimum force felt by the man $=\text{m}(\text{g}-\text{a}_\text{max})$$=50(10-7.9)$
$=105.0\text{N}$
$=10.5\text{kgf}$
Hence, the reading of the weighing machine varies between 10.5kgf and 69.5kgf.

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