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By the end of this section, you will be able to:
  • Define buoyant force
  • State Archimedes’ principle
  • Describe the relationship between density and Archimedes’ principle

When placed in a fluid, some objects float due to a buoyant force. Where does this buoyant force come from? Why is it that some things float and others do not? Do objects that sink get any support at all from the fluid? Is your body buoyed by the atmosphere, or are only helium balloons affected ( [link] )?

Figure A is a drawing of a ship anchor submerged underwater next to some sea shrubs. Figure B is a photo of a floating submarine with a wake on 3 sides. Figure C is a photo of many colored balloons floating in air.
(a) Even objects that sink, like this anchor, are partly supported by water when submerged. (b) Submarines have adjustable density (ballast tanks) so that they may float or sink as desired. (c) Helium-filled balloons tug upward on their strings, demonstrating air’s buoyant effect. (credit b: modification of work by Allied Navy; credit c: modification of work by “Crystl”/Flickr)

Answers to all these questions, and many others, are based on the fact that pressure increases with depth in a fluid. This means that the upward force on the bottom of an object in a fluid is greater than the downward force on top of the object. There is an upward force, or buoyant force    , on any object in any fluid ( [link] ). If the buoyant force is greater than the object’s weight, the object rises to the surface and floats. If the buoyant force is less than the object’s weight, the object sinks. If the buoyant force equals the object’s weight, the object can remain suspended at its present depth. The buoyant force is always present, whether the object floats, sinks, or is suspended in a fluid.

Buoyant force

The buoyant force is the upward force on any object in any fluid.

Figure is a schematic drawing of the cylinder filled with fluid and opened to the atmosphere on one side. An imaginary object with the surface area A, that is smaller than the surface area of the cylinder, is submerged into the fluid. Distance between the top of the fluid and the top of the object is h1. Distance between the top of the fluid and the bottom of the object is h2. Forces F1 and F2 are applied to the top and the bottom of the object, respectively.
Pressure due to the weight of a fluid increases with depth because p = h p g . This change in pressure and associated upward force on the bottom of the cylinder are greater than the downward force on the top of the cylinder. The differences in the force results in the buoyant force F B . (Horizontal forces cancel.)

Archimedes’ principle

Just how large a force is buoyant force? To answer this question, think about what happens when a submerged object is removed from a fluid, as in [link] . If the object were not in the fluid, the space the object occupied would be filled by fluid having a weight w fl . This weight is supported by the surrounding fluid, so the buoyant force must equal w fl , the weight of the fluid displaced by the object.

Archimedes’ principle

The buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes’ principle    is

F B = w fl ,

where F B is the buoyant force and w fl is the weight of the fluid displaced by the object.

This principle is named after the Greek mathematician and inventor Archimedes (ca. 287–212 BCE), who stated this principle long before concepts of force were well established.

Figure A is a drawing of a person submerged in water. Force wobj is expressed by the person, force Fb is applied by the water to the person. Figure B is a drawing in which the person is replaced by water. Now Force wfl is expressed by the water that replaced the person, force Fb remains the same.
(a) An object submerged in a fluid experiences a buoyant force F B . If F B is greater than the weight of the object, the object rises. If F B is less than the weight of the object, the object sinks. (b) If the object is removed, it is replaced by fluid having weight w fl . Since this weight is supported by surrounding fluid, the buoyant force must equal the weight of the fluid displaced.

Questions & Answers

a tire 0.5m in radius rotate at constant rate 200rev/min. find speed and acceleration of small lodged in tread of tire.
Tahira Reply
hmm
Ishaq
100
Noor
define the terms as used in gravitational mortion 1:earth' satellites and write two example 2:parking orbit 3:gravitation potential 4:gravitation potential energy 5:escping velocity 6:gravitation field and gravitation field strength
Malima Reply
what larminar flow
Rajab Reply
smooth or regular flow
Roha
Hii
Sadiq
scalar field define with example
Malik Reply
what is displacement
Isaac Reply
the change in the position of an object in a particular direction is called displacement
Noor
The physical quantity which have both magnitude and direction are known as vector.
Malik
good
Noor
Describe vector integral?
Malik
define line integral
Malik
Examples on how to solve terminal velocity
Louis Reply
what is Force?
Bibas Reply
ans:loading...
Lumai
the sideways pressure exerted by fluid is equal and canceled out.how and why?
Chaurasia
what is blackbody radiation
Syed Reply
Particles emitted by black holes
Lord
what is oscillation
Iwelomen Reply
Bernoulli's equation which applies a fluid flow states that P+h✓g+½PV²=k. where ✓=density. P=pressure. h=height. V= velocity. g=acceleration due to gravity. k= constant. Show that the equation is dimensionally constant and show the S.I unit for k.
amoni Reply
The nature of physics
Darshan Reply
what physics
Darshan
Physics deals with nature and its natural phenomenons
Sushant
physics explains more about mechanics and other natural phenomenon.
Ferdinand
define realitives motion
Zahid Reply
Relative motion is the calculation of the motion of an object with regard to some other moving object. Thus, the motion is not calculated with reference to the earth, but is the velocity of the object in reference to the other moving object as if it were in a static state.
Lansana
I am unable to access the mcq can someone help me with it?
Harkamal Reply
What is free fall?
Barham Reply
when an object is falling under the the influence of the earth gravitational force, the term is called free fall.
Bra
V=E½-P-½ where v; velocity, P; density and E; constant. Find dimension and it's units of E (constant)
michael Reply
ML-3
LAWAL
Practice Key Terms 2

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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