A man weighing 60 kg stands on the horizontal | vedclass

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(D) The maximum acceleration of the platform executing simple harmonic motion is given by $a_{max} = \omega^2 A$,where $\omega = 2\pi f$.Given $f = \f

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The spring balance reading fluctuates between $50\ kg$ and $70\ kg$.

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(D) The maximum acceleration of the platform executing simple harmonic motion is given by $a_{max} = \omega^2 A$,where $\omega = 2\pi f$.Given $f = \frac{2}{\pi}\ Hz$ and $A = 0.1\ m$,we have $\omega = 2\pi 	imes \frac{2}{\pi} = 4\ rad/s$.Thus,$a_{max} = (4)^2 	imes 0.1 = 16 	imes 0.1 = 1.6\ m/s^2$.The maximum pseudo-force acting on the man is $F_{max} = m \cdot a_{max} = 60\ kg 	imes 1.6\ m/s^2 = 96\ N$.In terms of weight in $kgf$,$F_{max} = \frac{96\ N}{9.8\ m/s^2} \approx 9.8\ kgf \approx 10\ kgf$.At the upper extreme position,the platform accelerates downwards,so the normal reaction $N = m(g - a_{max}) = 60 - 10 = 50\ kgf$.At the lower extreme position,the platform accelerates upwards,so the normal reaction $N = m(g + a_{max}) = 60 + 10 = 70\ kgf$.Therefore,the reading of the spring balance fluctuates between $50\ kg$ and $70\ kg$.

$A$ man weighing $60\ kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\ m$ and frequency $\frac{2}{\pi}\ Hz$. Which of the following statements is correct?

Similar Questions

$A$ horizontal platform with an object placed on it is executing $S.H.M.$ in the vertical direction. The amplitude of oscillation is $3.92 \times 10^{-3} \, m$. What must be the least period of these oscillations,so that the object is not detached from the platform (in $, s$)?

$A$ mass $m$ oscillates with simple harmonic motion with frequency $f = \frac{\omega}{2\pi}$ and amplitude $A$ on a spring with constant $K$. Therefore:

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