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 0.37 kg of turkey. The slices of turkey are weighed on a plate of mass 0.470 { m kg} placed atop a vertical spring of negligible mass and force constant of 204 N/m. The slices of turkey are dropped on the plate all at the same time from a height of 0.360 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 collision time is extremely small.

A) 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/s^2.

Explanation / Answer

k=204

Amplitude = maimal displacement

A=x =x1+x2

x1 - due to the plate: m1g=kx1 --> x1=0.470*9.8/204=0.0226 m

x2 - due to the dropped turkey: m2g(h+x2) = k(x2)^2/2,

solve the quadratic equation: 102*x2-3.626x2-1.3=0

--> x2=0.132

--> x=0.132+0.0226=0.1546 m

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