For lunch you and your friends decide to stop at the nearest deli and have a san

Question

For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.100kg of turkey. The slices of turkey are weighed on a plate of mass 0.400kg placed atop a vertical spring of negligible mass and force constant of 200 N/M . The slices of turkey are dropped on the plate all at the same time from a height of 0.250m . They make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (SHM). You may assume that the collision time is extremely small. What is the amplitude of oscillations of the scale after the slices of turkey land on the plate? Express your answer numerically in meters and take free-fall acceleration to be g= 9.80m/s .

Explanation / Answer

1. We must assume the scale is initially in equilibrium, so the net force which will extend the spring is due only to the mass of the ham accelerating under gravity. The mass of the plate does not contribute to the amplitude of the oscillation. F = m.a = 0.3kg x 9.8m/s^2 =0.98 N So spring extension = amplitude of oscillation = 0.98N / 200 N/m =4.9*10^-3m 2. The combined mass of ham + plate (0.5kg) determines the period of oscillation T T = 2.pi.SQRT(mass/spring constant) T = 2.pi.SQRT(0.5kg/200N/m)) T = 0.314 s

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