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smithg86
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[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.]
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.
[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
[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.
Homework Statement
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.
Homework 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
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.