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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

Charles's law

Charles’ law is an experimental gas law which describes how gases tend to expand when heated. When the pressure on a sample of a dry gas is held ... more

Nq bearing capacity factor

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This ... 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

Specific absorption rate (SAR)

Specific absorption rate calculates the rate at which energy is absorbed by the body when exposed to a radio frequency (RF) electromagnetic field. Specific ... more

Hot Air Balloon Lift

The hot air balloon is the oldest successful human-carrying flight technology. The first hot-air balloon flown in the United States was launched from the ... 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

Sorptivity

In 1957 John Philip introduced the term sorptivity and defined it as a measure of the capacity of the medium to absorb or desorb liquid by capillarity.
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Nγ bearing capacity factor (Terzaghi's theory)

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This ... more

Nc bearing capacity factor

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This ... more

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