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Air-to-cloth ratio

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First-order reaction (rate of disintegration)

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Relation between Polarization density and Electric field in various materials

In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a ... more

Michaelis–Menten enzyme kinetics (maximum reaction rate)

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics.The model takes the form of an equation describing the rate of enzymatic ... more

Relation between permeability and magnetic susceptibility

Permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of ... more

Bagnold number

he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first ... more

Bayes' theorem

In probability theory, a conditional probability measures the probability of an event given that (by assumption, presumption, assertion or evidence) ... more

Degree of Combined Leverage

In finance, leverage is a general term for any technique to multiply gains and losses.Most often it involves buying more of an asset by using borrowed ... 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

Kelvin–Helmholtz mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to ... more

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