Search results
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/
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. Gives a simple index of the ratio of the heat transfer resistances ... more
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
Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their ... more
Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the ... more
Many agencies and organizations (such as aerospace) define the margin of safety (MoS or M.S.) including the design factor, in other words, the margin of ... more
Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. Radiation pressure implies an interaction between ... more
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
Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, and invented in 1957 by C.W. Musser.
It is very ... more
The logarithmic mean temperature difference (also known as log mean temperature difference or simply by its initialism LMTD) is ... more
...can't find what you're looking for?
Create a new formula
(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?