For lunch you and your friends decide to stopat the nearest deli and have a sand

Question

For lunch you and your friends decide to stopat the nearest deli and have a sandwich made fresh for you with0.350 { kg}of turkey. The slices of turkey are weighed on a plateof mass 0.470 { kg} placed atop a vertical spring of negligiblemass and force constant of 201 { N/m}. The slices of turkey aredropped on the plate all at the same time from a height of 0.200 {m}. They make a totally inelastic collision with the plate and setthe scale into vertical simple harmonic motion (SHM). You mayassume that the collision time is extremely small.
1.What is the amplitude of oscillations A of the scale after theslices of turkey land on the plate?
2.What is the angular frequency of the oscillation? Remember{omega} = sqrt {k/m}
3.What is the period of oscillation T of the scale? For lunch you and your friends decide to stopat the nearest deli and have a sandwich made fresh for you with0.350 { kg}of turkey. The slices of turkey are weighed on a plateof mass 0.470 { kg} placed atop a vertical spring of negligiblemass and force constant of 201 { N/m}. The slices of turkey aredropped on the plate all at the same time from a height of 0.200 {m}. They make a totally inelastic collision with the plate and setthe scale into vertical simple harmonic motion (SHM). You mayassume that the collision time is extremely small.
1.What is the amplitude of oscillations A of the scale after theslices of turkey land on the plate?
2.What is the angular frequency of the oscillation? Remember{omega} = sqrt {k/m}
3.What is the period of oscillation T of the scale?

Explanation / Answer

m g h = 1/2 m v2    where v is thespeed of the slices when they strike the plate v2 = 2 g h      where h =.2 m m v = (m + M) V    after the slices strikes theplate V = m (2 g h) / (m + M) 1/2 (m + M) V2 + (m + M) g x = 1/2 kx2      where x is distance thespring is stretched m2 g h /(m + M) + (m + M) g x = 1/2k x2 Substitute and solve the quadratic for x x = A   the amplitude of vibration = (k / (m + M)      isthe frequency of the oscillation P = 1 / f = 2 /      for the period of oscillation Substitute and solve the quadratic for x x = A   the amplitude of vibration = (k / (m + M)      isthe frequency of the oscillation P = 1 / f = 2 /      for the period of oscillation

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