Question

Question 9 [3+ (6 + 2) = 11 marks] (a) A sand pendulum consists of a funnel shaped object filled with sand and suspended from a long string (not shown) as depicted in the diagram. As the pendulum swings back and forth in simple harmonic motion the sand gradually falls from the base of the funnel through a small hole in the bottom. Predict what will happen to the period of oscillation of the pendulum as mass is gradually lost. Explain briefly. You may assume that the mass of the string is negligible and ignore the effects of air resistance. Small hole (b) A pan containing beads is mounted on a spring and oscillates vertically in simple harmonic motion as shown in the following figure. If the frequency of oscillation of the pan is 60 Hz find the amplitude of the motion at which the beads will start to lift-off the pan. Show your reasoning and working. At what point in the motion will this occur? Explain your reasons for your answer. (ii)

Answer 1

sol" (a) Time period of oscillation e where ga acceleration due to greavity e = effective length effective length from petoot point carter of gravity given pendulum, initially when the for the when the funnel sand is full of effective length lo Period Т. when some part of funnel is empty, the center of gravity shifts downward and the effective in creases To the finally when funnel is completely empty. effective length again becomes lo Timepesied = 1 <T' Firstly the time period increases then decreases. again