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Desired radius of a curve

The equation for the desired radius of a curve, takes into account the factors of speed and superelevation (e). This equation can be algebraically ... more

Pitch diameter - in imperial units (gears)

A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part to transmit torque, in most cases with teeth ... more

Fractional bandwidth (RLC circuits)

The bandwidth as a fraction of the resonance frequency. Bandwidth is the difference between the upper and lower frequencies in a continuous set of ... more

Fractional shortening

Fractional shortening is the fraction of any diastolic dimension that is lost in systole. When referring to endocardial luminal distances, it is ... more

R-value (insulation) of a multi-layered installation - U.S. units

The R-value is a measure of thermal resistance, or ability of heat to transfer from hot to cold, through materials (such as insulation) and assemblies of ... 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/

Linear eccentricity of the hyperbola

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Cauchy–Lorentz distribution (probability density function)

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The probability density function (pdf), or density of a ... more

Shear coefficient (For solid circular cross-section beam)

Timoshenko beam model takes into account shear deformation and rotational inertia effects, making it suitable for describing the behavior of short sandwich ... more

Shear coefficient (For solid rectangular cross-section beam)

Timoshenko beam model takes into account shear deformation and rotational inertia effects, making it suitable for describing the behavior of short sandwich ... more

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