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Modulus of resilience

Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is ... more

Cantilever Euler Beam - Maximum Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more

Pressure dependence of the diffusion coefficient

Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration ... more

Von Mises yield criterion

The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant reaches a critical value. The von ... 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/

Speed of Sound (air, ideal gases)

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

Self-buckling critical height ( for a free-standing, vertical column)

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Load and Resistance Factor Design (LRFD) - Load combinations (eq1)

In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more

Depth of indentation of a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Vertical Pressure variation of the Atmosphere of Earth( exponential function of height)

Vertical pressure variation is the variation in pressure as a function of elevation. The vertical variation is especially significant, as it results from ... more

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