Consider an object with height h, mass M, and uniform cross sectional area A floating upright in a liquid with density p.

a.) Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium.

b.) A downward force of magnitude F is applied to the top of the object. At the new equilibrium position, how much farther below the surface of the liquid is the bottom of the object than it was in part (a)? (The assumption that F is small enough for some of the liquid to remain above the surface of the liquid should be made)

c) The result from part b should show that if the force is suddenly removed, the object will oscillate up and down in simple harmonicmotion. Calculate the period of this motion, in terms of the density p of the liquid and the mass M and cross-sectional area A of the object.

d.) A 1,500 kg cylindrical can buoy floats vertically in seawater (density 1.03 x 10^3 kg/m^3). The diameter of the buoy is 0.800m. Calculate the additional distance the buoy will sink when a 100 kg man stands on top.

e.) Calculate the period of the resulting vertical simple harmonic motion when the man dives off

f.) Calculate the period of oscillation of an ice cube 4.00 cm on a side floating in water with a density of 1.00 x 10^3 kg/m^3 if it is pushed down and released.

Solution Summary

This solution looks at the bouyance, harmonic motion and period of objects in a fluid.

The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared and is given in SI units) by a=-3.00 v^2 for v greater than 0. If the marble enters this fluid with a speed of 1.20 m/s, how long will it take before the marble's speed is reduced to half of its initial value?

Write a one to two page paper discussing your observations in terms of the principles of fluidmechanics that you learned in this module.
Required source :Buoyant force (simulation).
http://www.phy.ntnu.edu.tw/ntujava/index.php?topic=7

1. A laboratory receives a sample of a metallic alloy composed of aluminum and magnesium. The sample is a solid cylinder with a diameter of 2 cm and a length of 5 cm. Its mass is 15.70 g. What is its density? What is its specific gravity?
2. A boat has a dry weight of 3500 lbs. How many liters of water does it displace?

(Please refer to the attachment)
Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (see attachment) shows streamlines for the flow of an incompressible fluid in a tapered pipe of

Determine the specific gravity of spherical particles, D=(1/200 in), which drop through air at 33degrees F at a speed U of 0.3 ft/s. The drag force on a small sphere in laminar motion is given by 3(pi)(mu)DU.
This problem is in FluidMechanics by Victor Streeter.

1. Marlene has had lymph nodes removed from her armpit. Why would removal of lymph nodes cause swelling in her hand and arm?
2. Is lymph more similar to blood plasma or to interstitial fluid? Explain your answer.
3. (fill in the blank) Fluid from the legs passes through lymphatic vessels that enter the abdomen through the lumb

1. A fluid in an aquifer is 6.5 m above a reference datum, the fluid pressure is 1800 N/m2, and the flow velocity is 3.4 3 1025 m/s. The fluid density is 1.01 3 103 kg/m3.
(A) What is the total energy per unit mass?
(B) What is the total energy per unit weight? Show all work.