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/
Heat engines transform thermal energy, or heat into mechanical energy, or work. They cannot do this task perfectly, so some of the input heat energy is not ... more
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more
In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more
In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more
In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more
Effusion is the process in which a gas escapes through a small hole. This occurs if the diameter of the hole is considerably smaller than the mean free ... more
The Knoop hardness test /kəˈnuːp/ is a microhardness test – a test for mechanical hardness used particularly for very brittle materials or thin sheets, ... more
The center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero.
... more
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... 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?