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Runoff equation ( P >Ia)

Surface runoff is the water flow that occurs when the soil is infiltrated to full capacity and excess water from rain. The runoff is depended on the ... more

Latent Heat

Latent heat is the energy released or absorbed by a body or a thermodynamic system during a constant-temperature process. A typical example is a change of ... more

Burning Time

This formula calculates the duration of propulsion system burn which is required to achieve a desired ΔV.

... more

Monatomic ideal gas heat capacity at constant pressure

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting ... 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/

Standard Error

The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that ... more

Relation between the mean of logarithmized sample values and the mean of non-logarithmized sample values

a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. A random ... more

Relation between the standard deviation of logarithmized sample and the non-logarithmized sample values

Log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. The standard ... more

Margin of error - Effect of population size

The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. The larger the margin of error, the less ... more

Hot Air Balloon Lift

The hot air balloon is the oldest successful human-carrying flight technology. The first hot-air balloon flown in the United States was launched from the ... more

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