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Mass fraction

In a mixture, the mass fraction is the amount of mass of one substance, divided by the mass of the total mixture. The sum of all the mass fractions is ... more

The mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity transferred at that electrode. ... more

Amount of Substance

Amount of substance (n) is the number of atoms, molecules, ions, or other specified group of entities present in a compound. It is the ratio of Mass / ... more

Density

The density of a material is defined as its mass per unit volume. For a pure substance the density has the same numerical value as its mass concentration. ... more

Wet bulk density of soil (total bulk density)

Bulk density is a property of powders, granules, and other “divided” solids, especially used in reference to mineral components (soil, gravel), ... more

Number density (Relation to Mass density)

Number density is an intensive quantity used to describe the degree of concentration of countable objects. For atoms or molecules of a well-defined ... more

Mixing ratio (mass ratio)

chemistry and physics, the dimensionless mixing ratio is defined as the abundance of one component of a mixture relative to that of all other components. ... more

Worksheet 296

(a) Calculate the buoyant force on 10,000 metric tons (1.00×10 7 kg) of solid steel completely submerged in water, and compare this with the steel’s weight.

(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00×10 5 m 3 of water?

Strategy for (a)

To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table [insert table #] We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight

First, we use the definition of density to find the steel’s volume, and then we substitute values for mass and density. This gives :

Density

Because the steel is completely submerged, this is also the volume of water displaced, Vw. We can now find the mass of water displaced from the relationship between its volume and density, both of which are known. This gives:

Density

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

Force (Newton's second law)

The steel’s weight is 9.80×10 7 N , which is much greater than the buoyant force, so the steel will remain submerged.

Strategy for (b)

Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.

The mass of water displaced is found from its relationship to density and volume, both of which are known. That is:

Density

The maximum buoyant force is the weight of this much water, or

Force (Newton's second law)

Discussion

The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics

Dry bulk density of soil

Bulk density is a property of powders, granules, and other “divided” solids, especially used in reference to mineral components (soil, gravel), chemical ... more

Molality

In chemistry, the molality of a solution is defined as the amount of substance of solute,, divided by the mass of the solvent, (not the mass of the solution)

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