Q. 35

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 person’s 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?

Answer :

Given:


Mass = 50kg


Harmonic frequency = 2.0


angular velocity


Amplitude A = 5.0 cm


The weighing machine will measure the normal reaction of the body as weight.


Now let be the acceleration of the platform



When the platform raises up,



From the above free body diagram we get the following force balance equation,



-----(1)


where N is the normal reaction


which shows that the weight measured by the machine will be less than the actual, since the machine shows the normal reaction and not mg


When the platform moves down,



From the above free body diagram we get the following force balance equation,



-----(2)


where N is the normal reaction


which shows that the weight measured by the machine will be more than the actual, since the machine shows the normal reaction and not mg


a) In the cases when platform rises and drops the weight measured are different. answer to part (a) is yes


b) Since the reading by the machine depends on the Normal reaction. Therefore, it will be maximum and minimum when the normal reaction is maximum and minimum respectively.


For minimum reading we put given values in equation (1),



For maximum reading we put given values in equation (1),



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