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.

KE_{0} = 0 (velocity is zero)

KE_{f} = (1/2)mv_{2}

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/s^{2}

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Simple Harmonic Motion of Vertical Springs concept. You can view video lessons to learn Simple Harmonic Motion of Vertical Springs. Or if you need more Simple Harmonic Motion of Vertical Springs practice, you can also practice Simple Harmonic Motion of Vertical Springs practice problems.