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?

This is a long answer type question as classified in NCERT Exemplar

(a) The weight of the body changes during oscillations.

(b) Considering the situations in two extreme positions

we can say mg-N= ma

so at the highest point the platform is accelerating downward.

N=mg-ma

a=w²A

N=mg-mw²A

A= amplitude of motion m=50kg v=2m/s

w=2 $\pi v=4\pi rad/s$

 A= 5cm = 5 $\times {10}^{-2}m$

N= 50 $\times 9.8-50\times {\left(4\pi \right)}^2\times 5\times {10}^{-2}=95.5N$

When it is accelerating towards mean position that is vertically upwards

N-mg=ma=Mw²A

N=mg+mw²A

N=m (g+w²A)

N= 50 [9.8+ ${\left(4\pi \right)}^2\times 5\times {10}^{-2}$ ]

N= 884N

Machine reads the normal reaction

Maximum weight =884N

Minimum weight=95.5N

<p><span data-teams="true">This is a long answer type question as classified in NCERT Exemplar</span></p><p><strong> (a) </strong>The weight of the body changes during oscillations.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745559912phppC97Fu.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745559300php2na7aF.jpeg" alt="" width="238" height="134"></picture></div><div><p><strong> (b)</strong> Considering the situations in two extreme positions</p><p>we can say mg-N= ma</p><p>so at the highest point the platform is accelerating downward.</p><p>N=mg-ma</p><p>a=w²A</p><p>N=mg-mw²A</p><p>A= amplitude of motion m=50kg v=2m/s</p><p>w=2<span contenteditable="false"> <math> <mi>π</mi> <mi>v</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mo>/</mo> <mi>s</mi> </math> </span></p><p>&nbsp;A= 5cm = 5<span contenteditable="false"> <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> <mi>m</mi> </math> </span></p><p>N= 50<span contenteditable="false"> <math> <mo>×</mo> <mn>9.8</mn> <mo>-</mo> <mn>50</mn> <mo>×</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>95.5</mn> <mi>N</mi> </math> </span></p></div></div><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745559912phppC97Fu_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745559912phppC97Fu.jpeg" alt="" width="243" height="114"></picture></div><div><p>When it is accelerating towards mean position that is vertically upwards</p><p>N-mg=ma=Mw²A</p><p>N=mg+mw²A</p><p>N=m (g+w²A)</p><p>N= 50 [9.8+<span contenteditable="false"> <math> <msup> <mrow> <mrow> <mo> (</mo> <mn>4</mn> <mi>π</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> </span> ]</p><p>N= 884N</p><p>Machine reads the normal reaction</p><p>Maximum weight =884N</p><p>Minimum weight=95.5N</p></div></div>

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