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Saturated unit weight

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

Moist unit weight

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

Submerged unit weight

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

Degree of saturation

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 (density related)

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

Porosity

The volume of the voids of a soil over the total volume of the sample defines the porosity of a soil. Used in geology, hydrogeology, soil science, and ... more

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

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

Specific gravity of solids

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

Relative density of soil

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

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