question_answer 60)

                  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?

Answer:

                  (a) Weight increases when object accelerates upward and weight decreases when object accelerates downward. In this case, person will be accelerated up and down during the oscillation of the platform. Hence, his weight will change during the oscillation. (a) Maximum acceleration of the platform,                 \[a=\,{{\omega }^{2}}r\]                 \[4{{\pi }^{2}}\,{{v}^{2}}r=4\times \,{{(3.14)}^{2}}\times \,4\times 5\times \,{{10}^{-2}}\]                 \[=7.89\,m\,{{s}^{-2}}\]                 \[\therefore \] Maximum reading in the machine (i.e., maximum weight)                            \[=Mg+Ma=M(g+a)\]                 \[=50(9.8+7.89)=884.5\text{ }N\]                 Minimum weight \[=M(g-a)\]                 \[=50(9.8-7.89)=95.5\text{ }N\]