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Freefall in Uniform Gravitational Field with Air Resistance (velocity)

Free fall is any motion of a body where its weight is the only force acting upon it. In Uniform gravitational field with air resistance the air resistance ... more

Worksheet 290

Find the terminal velocity of an 85-kg skydiver falling in a spread-eagle position.

Terminal Velocity (without considering buoyancy)
Rectangle area

where Vt is the terminal velocity, m is the mass of the skydiver, g is the acceleration due to gravity, Cd is the drag coefficient, ρ is the density of the fluid through which the object is falling, and A is the projected area of the object.

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/

where h is skydiver height and w the width at “spread-eagle” position

Rayleigh Number

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy driven flow (also known as free convection or ... more

Alfvén velocity (in SI)

In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring ... more

Terminal velocity (potato-shaped obgject)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Alfvén velocity

In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring ... more

Rayleigh number (for geophysical applications - related to bottom heating of the mantle from the core)

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more

Gravity Acceleration by Altitude

The gravity of Earth, which is denoted by g, refers to the acceleration that the Earth imparts to objects on or near its surface due to gravity. In SI ... more

Energy Density (magnetic field)

Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... 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/

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