For lunch you and your friends decide to stop at the nearest deli and have a san
ID: 1702852 • Letter: F
Question
For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.400kg of turkey. The slices of turkey are weighed on a plate of mass 0.490kg placed atop a vertical spring of negligible mass and force constant of 287N/m . The slices of turkey are dropped on the plate all at the same time from a height of 0.400m . 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 = 9.80m/s^2 .
What is the angular frequency of the oscillation? Remember w=sqrt(k/m).
What is the period of oscillation T of the scale?
Express your answer numerically in seconds.
Explanation / Answer
Given that h = 0.4 m m = 0.40 kg M = 0.490 kg k = 287 N/m --------------------------------------------------------------------------------------------------- According to conservation of energy we have m g h = 0.5 m v^2 ==> v = [2 g h]^1/2 ---------------------------------------------------------------------------------------------------- When the slices strikes the plate, According to conservation of momentum we have m v = (m + M) V after V = m (2 g h)^1/2 / (m + M) --------------------------------------------------------------------------------------------- Therefore applying conservation of energy to whole system we have 0.5 (m + M) V^2 + (m + M) g x = 0.5 kx^2 ==> 2mg h /(m + M) + (m + M) g x = 0.5k x^2 Substitute the values and solve the quadratic for x --------------------------------------------------------------------------------------------- Amplitude of the vibration = x The frequency of the oscillation ? = {k / (m + M)}^1/2 Period T = 2 p / ? --------------------------------------------------------------------------------------- Substitute values in above equations
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