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Magnetic susceptibility

The magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied ... more

Ideal gas - isobaric process

An isobaric process is a thermodynamic process in which the pressure stays constant: ΔP = 0. The heat transferred to the system does work, but also changes ... more

Characteristic Length

In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a ... more

Speed of sound in sea water (UNESCO equation)

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. The speed of sound in seawater depends ... more

Internal energy isobaric process

An isobaric process is a thermodynamic process in which the pressure stays constant: ΔP = 0. The heat transferred to the system does work, but also changes ... more

X-Coordinate of the vertex, of the parabola of a Quadratic Function

Parabolas with axes of symmetry parallel to the y-axis have equations of the form y=ax^2+bx+c.
The x-coordinate and y-coordinate at the vertex can be ... 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/

Luminosity of a star by the luminosity of the Sun relationship

Dividing the luminosity of a star by the luminosity of the Sun (also know as a solar luminosity) and cancelling constants, we obtain a relationship related ... more

Radius of Inertial circle ( by Coriolis effect)

In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame.
An air or water mass moving with ... more

Magnitude of proper motion

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

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