[This was a 4 part question. The first 2 parts were correctly done (so I didn't show much work for them). I'm not sure about the last 2 parts. I only need help with the last 2 parts.](adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A closed hollow cylinder of length L = 0.5 m, cross sectional area A= 0.0004 m^2 and a negligible mass has a lead weight of mass m=0.1 kg inside at the bottom so that it floats vertically when placed in water.

[1st part]

Determine the distance, d, from the bottom of the cylinder to the surface of the water.

I calculated d = 0.25m

[2nd part]

The cylinder is now pushed down a distance x from the equilibrium position, d, determined above. What is the additional force on the cylinder trying to restore it to its equilibrium position?

I calculated F = 3.924x

[3rd part]

What is the period of the vertical oscillations of the cylinder?

[4th part]

Estimate the period of rotational oscillations, where the axis of the cylinder oscillates back and forth in a vertical plane.

2. Relevant equations

[For part 1]

(.1kg mass) = (mass of displaced water) = (density of water)(volume of submersed part of cylinder)

[For part 2]

(.1 kg + F) = (new displaced volume of water)(density of water)

[For part 3]

w = (k/m)^(1/2)

T = (2pi)/w

[For part 4]

(torque) = -k(theta)

w = (k/I)^(1/2)

T = 2pi/w

3. The attempt at a solution

[Part 3]

T = 2pi/w = 2pi(m/k)^(1/2) = 2pi(.1/3.924)^(1/2) = 1.00303 seconds [?]

[Part 4]

T = 2pi/w = 2pi/ 25.0567 = 0.250758 seconds [?]

Are these answers correct? Thanks.

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# Oscillation/Buoyancy Question

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