# Search results

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value ... more

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

In crystallography, the triclinic crystal system is one of the 7 crystal systems. A crystal system is described by three basis vectors. In the triclinic ... more

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes ... more

In crystallography, atomic packing factor (APF), packing efficiency or packing fraction is the fraction of volume in a crystal ... more

In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more

Collision theory qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. The collision theory states ... more

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after ... more

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 :

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:

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

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:

The maximum buoyant force is the weight of this much water, or

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/

...can't find what you're looking for?

Create a new formula
(a)Calculate the buoyant force on10,000 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 displace1.00×10 5 mof water?^{3}