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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

what is quantam
pamit Reply
quantum is a division of mechanics
Baje
what is friction
Muhammad Reply
a force act by surface between two bodies whose are always oppose the relative motion .....
Raghav
when two rough bodies are placed in contact and try to slip each other ... than a force act them and it's ippse the relative motion between them
Raghav
thats friction force and roughnes of both bodies is define friction of surface
Raghav
what is a progressive wave
sheriff-deen Reply
What is the wake for therapist
Ife Reply
can u like explain your question with clear detail
Chikamso
who would teach me vectors?
Tintin Reply
what's chemistry
Esther Reply
branch of science dt deals with the study of physical properties of matter and it's particulate nature
Josiah
Good
Daniel
actually
Nathz
Y acctually do u hav ur way of defining it? just bring ur iwn idear
Daniel
well, it deals with the weight of substances and reaction behind them as well as the behavior
Josiah
buh hope Esther, we've answered ur question
Josiah
what's ohms law
CHIJIOKE
ohms law states that, the current flowing through an electric circuit is directly proportional to the potential difference, provided temperature and pressure are kept constant
Josiah
what is sound
James
ohms law states that the resistance of a material is directly proportional to the potential difference between two points on that material, if temperature and other physical conditions become constant
Chikamso
How do I access the MCQ
Abraham Reply
As I think the best is, first select the easiest questions for you .and then you can answer the remaining questions.
lasitha
I mean I'm unable to view it
Abraham
when I click on it, it doesn't respond
Abraham
ohhh,try again and again ,It will be showed
lasitha
okay
Abraham
what is centripetal force
Don Reply
هي قوة ناتجة من الحركة الدائرية ويكون اتجاهها إلى المركز دائماً
meaning of vector quantity
Felix Reply
vector quantity is any quantity that has both magnitude in terms of number (units) and direction in terms of viewing the quantity from an origin using angles (degree) or (NEWS) method
LEWIS
vector quantity is physical quantity has magnitude and direction
vector is a quantity that is use in measuring size of physical properties and their direction
Bitrus
what difference and similarities between work,force,energy and power?
Anes Reply
I need the best answer
Anes
power
mehreen
power
saba
enery is the ability to do work. work is job done, force is a pull or push. power has to do with potential. they belong to different categories which include heat energy, electricity.
Andrew
force refers to a push or pull... energy refers to work done while power is work done per unit time
Shane
mathematically express angular velocity and angular acceleration
Mario Reply
it depends on the direction. an angular velocity will be linear and angular acceleration will be an angle of elevation.
Andrew
The sonic range finder discussed in the preceding question often needs to be calibrated. During the calibration, the software asks for the room temperature. Why do you suppose the room temperature is required?
Shaina Reply
Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See [link] .) (a) Calculate the echo times for temperatures of 5.00°C5.00°C and 35.0°C.35.0°C. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty an
Shaina
give a reason why musicians commonly bring their wind instruments to room temperature before playing them.
Shaina
The ear canal resonates like a tube closed at one end. (See [link]Figure 17_03_HumEar[/link].) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be 37.0°C,37.0°C, which is the same as body tempe
Shaina
By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0°C10.0°C to 30.0°C30.0°C ? That is, find the ratio of the frequencies at those temperatures.
Shaina
what are vector quantity
Aondover Reply
Quantities that has both magnitude and direction
NNAEMEKA
what is lenses
Rhoda
vector quantities are those physical quantites which have magnitude as well as direction and obey the laws of vector algebra.
Huzaif
electric current has both magnitude and direction but it doesn't obey the laws of vector algebra, hence it is not a vector quantity.
Huzaif
what is momentum
Thomas Reply
Momentum=mv
Nana
what is dimension
Ahmad Reply
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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