Archimedes principle?

Question

1. When solids are dissolved in a liquid the solid take up the spaces between the liquid molecules. If I have 2 containers and I dissolve 50grams of salt in one and 50 grams of sugar in the other, which container would provide your aluminum block with a greater buoyancy force (assume both completely dissolve)?
Help please!!

Answer 1

The buoyancy force equals the density of the fluid (ρ) times the volume of the submerged object (V) times standard gravitational constant (g, which equals 9.80 N/kg).

Fb = ρVg

Basically, the buoyancy force acting on the aluminum block equals the weight of water displaced by the block.

weight = (mass)*(acceleration)

weight = (density)*(volume)*(acceleration)

Since the chemicals are contained in the aluminum block, and aren't in the water directly, the only effect they have is that they change the mass of the aluminum block, and NOT the volume of the block. Since both the salt and the sugar are 50 g each, the densities will be the same, and both will result in the same buoyancy force.

Answer 2

Archimedes' principle states that the buoyant force (not the total force) on an object is equal to the weight of the fluid displaced by the object.

When you dissolve sugar or salt in water, the volume of the water essentially doesn't change. However, the density of the solution increases. If you have a submerged aluminum block, the buoyant force on that block will equal the weight of the fluid displaced by the block.

weight = mass * acceleration = volume * density * acceleration

Since the mass of the fluid in each container would increase by 50 grams in either case, and (I'm assuming) the amount of water is the same in each container, the density of the solutions will be the same. Each will provide the same buoyant force to the aluminum block.