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Darby-Melson equation (for Buckingham-Reiner equation)

Although an exact analytical solution of the Buckingham-Reiner equation can be obtained because it is a fourth order polynomial equation in f, due to ... more

Daniell cell

The Daniell cell is a type of electrochemical cell consisted of a copper pot filled with a copper sulfate solution, in which was immersed an unglazed ... more

Density of an ideal gas

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The density of gases is strongly affected by ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

Descartes' theorem ( internally tangent circle to three given kissing circles)

n geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic ... more

Henry's law constant (dimensionless)

Henry’s law states : “At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly ... more

Charge of mole of ions goes into solution

If a mole of ions goes into solution the charge through the external circuit depends on the number of moles or ions and the “Faraday constant” ... 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/

Kepler's equation

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

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