Weighing Lunch Constants PartA For lunch you and your friends decide to stop at

Question

Weighing Lunch Constants PartA For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.100 kg of turkey. The slices of turkey are weighed on a plate of mass 0.400 kg 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 0.250 m. They make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (SHM). You may assume that the What is the amplitude of oscillations A 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 9.80 m/ View Available Hint(s) collion time is extremely small. A= 495 in Submit Incorrect: Try Again: 3 attempts remaining

Explanation / Answer

For vertical spring

mg = kx => x = mg/k = 0.1 x 9.81/200 = 0.005 m

we know from conservation of momentum

m1v1 = (m1 + m2)vf

m1 sqrt (2 g h1) = (m1 + m2)v2

v2 = m1 sqrt (2 g h1)/(m1 + m2)

v2 = 0.1 sqrt (2 x 9.81 x 0.25)/(0.1 + 0.4) = 0.443 m/s

From conservation of energy

1/2(m1 + m2)vf^2 + 1/2 kx^2 = 1/2 kA^2

(0.1 + 0.4) x 0.443^2 + 200 x 0.005^2 = 200 x A^2

A = sqrt (0.0005155) = 0.0227 m

A = 0.0227 m

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