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Ideal gas law (Molar form)

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, ... more

Number density (Relation to Molar concentration)

Number density is an intensive quantity used to describe the degree of concentration of countable objects. For any substance, the number density n can be ... more

Fick principle (calculation of cardiac output)

The essence of the Fick principle is that blood flow to an organ can be calculated using a marker substance if the following information is known:
... more

Raoult's law

Raoult’s law is a law of thermodynamics and states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the ... more

Schwarzschild radius

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the ... more

Diffusion Coefficient for two different gases (related to Fick's laws)

Diffusion is the net movement of a substance (e.g., an atom, ion or molecule) from a region of high concentration to a region of low concentration. For two ... more

Gay-Lussac's Law (Pressure-temperature law)

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas’ absolute temperature. If a gas’s temperature ... 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
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

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

Gravitational Binding Energy - spherical mass of uniform density

The gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of ... more

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