Question

A person normally weighing 50 kg stands on a massless platform which oscillated up and down harmonically at a frequency of 2.0 s^-1 and an amplitude 5.0 cm. A weighting 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 1

(a) Yes, change of weight will be there,

(b) Given mass = m = 50 kg, v = 2s^-1 , A = 5 cm = 0.05 m

Let the platform vibrate between two extreme positions O

P and Q about mean position O.

a_max = Maximum acceleration towards mean position O

a_max = w²A = (2πv)² A

= 7.9ms^-1

At P, restoring force (ma_max) and weight (mg) are directed towards mean position. so net weight at P given by

W₁ = mg + ma_max = m(g + a_max)

= 50(9.8 + 7.9) = 885 N

Similarly, net weight at Q

W₂ = mg − ma_max = m(g − a_max)

= 50(9.8 − 7.9) = 95N

Weight is maximum at top position and minimum at lowermost position.