physics homework questions?

Question

I'm having trouble with the difference between the effect of weight and volume on flotation..

1. Compared with an empty ship, would a ship loaded with a cargo of Stryrofoam sink deeper into the water or rise in the water? Defend your answer.

2. A barge filled with scrap iron is in a canal lock. If the iron i thrown overboard, does the water level at the side of the lock rise, fall, or remain unchanged? Explain

3. Suppose that you are given the choice between two life preservers that are identical in size, the first a light one filled with Styrofoam and the second a very heavy one filled with gravel. If you submerge thse life preservers in the water, upon which will the buoyant force be greater? (the one filled with gravel right?) Upon which will the buoyant force be ineffective (Styrofoam?) Why are your answers different?

Answer 1

1. Styrofoam or it all depends on the weight and volume of the fluid displaced.
General equation taking buoyant of water and air into consideration is the total force on the object F
F=W-Fbw - Fba
W=mg (weight of the object)
Fbw - Buoyant force due to displacement in water
Fba - Buoyant force due to displacement in air

While
Fbw - weight of the water displaced = Total volume of the water displaced times density of water
However
Fba - weight of the air displaced = Total volume of the objects times density of air.

2. If you remove the scrap the barge will rise, water level will fall since less water is displaced. By dropping the scrap into the canal lock the level will rise, but will be less then before you removed the scrap from the barge since the density of iron is larger then water. Volume of water will rise to
V=(p(iron) x mass of the iron ) p(water)
p(iron) - density of iron
V – volume of water.

3. The density of Styrofoam is 100kg/m^3 stone is say about 2,200 kg/m^3
Styrofoam is 2,200/100 = 22 times lighter than stone and
Styrofoam is 1,000/100 = 10 times lighter than water.
Stone is 2,200/1000 = 2.2 times heavier that water.

Any questions?