Simple Harmonic Motion of Vertical Springs Video Lessons

Concept

# Problem: For lunch, you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 kg of Italian ham. The slices of ham are weighed on a plate of mass 0.400 kg placed atop a vertical spring of negligible mass and force constant of 200 N/m. The slices of ham are dropped on the plate all at the same time from a height 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 that the collision time is extremely small.What is the amplitude of oscillation A of the scale after the slices of ham land on the plate?Express your answer numerically in meters and take free-fall acceleration to be g = 9.80m/s2

###### FREE Expert Solution

Gravitational potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

The potential energy of a simple harmonic oscillator:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{K}}{{\mathbf{A}}}^{{\mathbf{2}}}}$

Momentum:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

We'll use the conservation of kinetic and gravitational potential energies to solve for the final velocity of the slices.

KE0 = 0 (velocity is zero)

KEf = (1/2)mv2

93% (233 ratings)
###### Problem Details

For lunch, you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 kg of Italian ham. The slices of ham are weighed on a plate of mass 0.400 kg placed atop a vertical spring of negligible mass and force constant of 200 N/m. The slices of ham are dropped on the plate all at the same time from a height 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 that the collision time is extremely small.

What is the amplitude of oscillation A of the scale after the slices of ham land on the plate?

Express your answer numerically in meters and take free-fall acceleration to be g = 9.80m/s2