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 0.240 of turkey. The slices of turkey are weighed on a plate of mass 0.480 placed atop a vertical spring of negligible mass and force constant of 236 . The slices of turkey are dropped on the plate all at the same time from a height of 0.330 . 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?

Explanation / Answer

speed of turkey when it hits scale = sqrt(2gh) = sqrt(2*9.8*.33) = 2.543 m/s

speed of scale and turkey after collision = mass turkey * speed turkey / total mass =

= 0.240 * 2.543 / (0.240 + 0.480) = 0.84774 m/s

This is the max speed of the oscillations. Now

amplitude = max speed * sqrt (total mass / k) = 0.84774 * sqrt(0.720 / 236) =

= 0.04683 meters = 4.683 cm

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