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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

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

Mole fraction

In chemistry, the mole fraction is defined as the amount of a constituent divided by the total amount of all constituents in a mixture.The mole fraction ... 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

Mass ratio

The mass ratio is defined as the mass of a constituent divided by the total mass of all other constituents in a mixture.

... more

Propellant mass fraction

In aerospace engineering, the propellant mass fraction is the portion of a vehicle’s mass which does not reach the destination, usually used as a ... more

Mass fraction (relation between mass and molar concentration)

In chemistry, the mass concentration is defined as the mass of a constituent divided by the volume of the mixture. The mass concentration of a component ... more

Porosity (density related)

Porosity or void fraction is a measure of the void (i.e., “empty”) spaces in a material, and is a fraction of the volume of voids over the ... 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

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