? w12-Post: Osctations tem 11 What is the ampli tude of oscilation A of the scal

Question

? w12-Post: Osctations tem 11 What is the ampli tude of oscilation A of the scale after the sices of ham land on the plate? Express your answer numerically in meters and take free-fall acceleration to be g 9.0m/s For lunch you and your friends decide to stop at the and have a sandwich made wth 0 300 kg of itali an ham The sices of ham are weighed on a plake of mass 0.400 kg placed alop a vertical spring of negigible mass and force constant of 200 N/. The slices of ham are dropped on the plate al at the same time from a heigt 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 thatl the colision Sme is extremely smal View Available Hints) A 0.0196 Previous Answers X Incorrect: Try Again; 5 attempts remaining Part B What is the period of oscillation T of the scale? Express your answer numerically in seconds 80 2 4

Explanation / Answer

Given,

m1 = 0.3 kg ; M = 0.4 kg ; k = 200 N/m ; = 0.25 m

m1g = kx=> x = m1g/k = 0.3 x 9.81/200 = 0.015 m

v1 = sqrt(2 g h) = sqrt (2 x 9.81 x 0.25) = 2.21 m/s

from conservation of momentum

Pi = Pf

m1v1 = (m1 + m2)vf

vf = m1v1/(m1 + m2)

vf = 0.3 x 2.21/(0.3 + 0.4) = 0.95 m/s

from conservation of energy

1/2(m1 + m2)vf^2 + 1/2 k x^2 = 1/2 k A^2

(0.3 + 0.4)0.95^2 + 200 x 0.015^2 = 200 x A^2

A = 0.0582 m

b)T = 2 pi sqrt[(m1 + m2)/k]

T = 2 x 3.14 sqrt[(0.3 + 0.4)/200] = 0.37 s

Hence, T = 0.37 s

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