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In fluid mechanics, specific weight represents the force exerted by gravity on a unit volume of a fluid. Specific weight can be used as a characteristic ... more

In fluid mechanics, specific weight represents the force exerted by gravity on a unit volume of a fluid. Specific weight can be used as a characteristic ... more

In fluid mechanics, specific weight ( or unit weight ) represents the force exerted by gravity on a unit volume of a fluid. Specific weight can be used as ... more

Soil is the mixture of minerals, organic matter, gases, liquids, and the myriad of organisms that together support plant life. The ratio of the volume of ... more

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

Bulk density is a property of powders, granules, and other “divided” solids, especially used in reference to mineral components (soil, gravel), chemical ... more

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 :

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:

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

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:

The maximum buoyant force is the weight of this much water, or

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/

Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to ... more

Bulk density is a property of powders, granules, and other “divided” solids, especially used in reference to mineral components (soil, gravel), ... more

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(a)Calculate the buoyant force on10,000 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 displace1.00×10 5 mof water?^{3}