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  • A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s ^–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.

A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s-1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
(a) Will there be any change in weight of the body, during the oscillation?
(b) If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?

Answers (1)

Due to normal reaction ‘N’, there will be weight in weight machine. 

Let us consider the top positions of the platform, both the forces, due to the weight of the person and oscillator acts downwards.

Thus, the motion will be downwards.

Let us consider, acceleration = a

ma = mg – N        …….. (i)

Now, when the platform moves upwards from its lowest position,

ma = N – mg       …….. (ii)

Now, acceleration of oscillator is

a = \omega ^{2}A

From (i),

N = mg - m \omega ^{2}A

Where,

Amplitude = A

Angular frequency = ω &

Mass of oscillator = m

\omega =2 \pi v

   = 4 \pi rad /s

A = 5cm

  = 5 \times 10^{-2}m

m = 50 kg

N = 50 \times 9.8 - 50 \times 4\pi \times 4\pi \times 5 \times 10^{-2}

  = 50[ 9.8 -16\pi ^{2} \times 5\times 10^{-2}]

 = 50 \times 1.91

   = 95.5 N

Thus, the minimum weight is 95.5 N.

From (ii),

N – mg = ma

Now, for upward motion from the lowest point of the oscillator,

N = m (a + g)

   = m [ 9.81 + \omega ^{2}A] = \omega ^{2}A

= 50 [9.81 + 7.89]

= 50 [17.7]

= 885 N

Therefore, during oscillation, there is a change in the weight of the body.

Also, maximum weight = 885 N, when the platform moves to upward direction from lowest direction & minimum weight = 95.5 N, when the platform moves to downward direction from the highest point.
 

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