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Speed of Sound (air, ideal gases) - relative to molar mass

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... 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

Diatomic ideal gas heat capacity at constant volume

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting ... more

Rule of Mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Inverse Rule of Mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Graham's Law of Effusion

Effusion is the process in which a gas escapes through a small hole. This occurs if the diameter of the hole is considerably smaller than the mean free ... more

Drift velocity in a current-carrying metallic conductor

The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. In general, an electron will 'rattle ... more

Volume Fraction of the Fibers (Rule of mixtures)

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... 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/

Peng–Robinson equation of state (a component)

refer to Peng–Robinson equation of state.

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