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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

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Clifton Reply
list and explain the 3 ways of charging a conductor
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conduction convention rubbing
Asdesaw
formula of magnetic field
Yonas Reply
Integral of a vector
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define surface integral of a vector?
Rahat
the number of degree freedom of a rigid body in2-dimantion is:
Raj Reply
1
Nathan
A block (A) of weight 5 kN is to be raised by means of a 20° wedge (B) by the application of a horizontal force (P) as shown in Fig.1. The block A is constrained to move vertically by the application of a horizontal force (S). Find the magnitude of the forces F and S, when the coefficient of fricti
Danilo
A body receives impulses of 24Ns and 35Ns inclined 55 degree to each other. calculate the total impulse
Sukpen Reply
A body receives impulses of 24Ns and 35Ns inclined 55 degree to each other. calculate the total impulse
Previous
twenty four square plus thirty-five square minus to multiple thirty five twenty four and equal answer number square Via this equation defined Total Total impulse
Cemal
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define surface integral vector?
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The uniform boom shown below weighs 500 N, and the object hanging from its right end weighs 400 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom?
Jave Reply
A 11.0-m boom, AB , of a crane lifting a 3000-kg load is shown below. The center of mass of the boom is at its geometric center, and the mass of the boom is 800 kg. For the position shown, calculate tension T in the cable and the force at the axle A .
Jave
what is the S.I unit of coefficient of viscosity
Biam Reply
Derived the formula of Newton's law of universal gravitation Fg=G(M1M2)/R2
Monychol Reply
hi
Asdesaw
yes
Cemal
a non-uniform boom of a crane 15m long, weighs 2800nts, with its center of gravity at 40% of its lenght from the hingr support. the boom is attached to a hinge at the lower end. rhe boom, which mAKES A 60% ANGLE WITH THE HORIZONTAL IS SUPPORTED BY A HORIZONTAL GUY WIRE AT ITS UPPER END. IF A LOAD OF 5000Nts is hung at the upper end of the boom, find the tension in the guywire and the components of the reaction at the hinge.
dangly Reply
what is the centripetal force
Malok Reply
Of?
John
centripetal force of attraction that pulls a body that is traversing round the orbit of a circle toward the center of the circle. Fc = MV²/r
Sampson
centripetal force is the force of attraction that pulls a body that is traversing round the orbit of a circle toward the center of the circle. Fc = MV²/r
Sampson
I do believe the formula for centripetal force is F=MA or F=m(v^2/r)
John
I mean the formula is Fc= Mass multiplied by square of velocity all over the Radius of the circle
Sampson
Yes
John
The force is equal to the mass times the velocity squared divided by the radius
John
That's the current chapter I'm on in my engineering physics class
John
Centripetal force is a force of attraction which keeps an object round the orbit towards the center of a circle. Mathematically Fc=mv²/r
Adebileje
In Example, we calculated the final speed of a roller coaster that descended 20 m in height and had an initial speed of 5 m/s downhill. Suppose the roller coaster had had an initial speed of 5 m/s uphill instead, and it coasted uphill, stopped, and then rolled back down to a final point 20 m bel
tan Reply
A steel lift column in a service station is 4 meter long and .2 meter in diameter. Young's modulus for steel is 20 X 1010N/m2.  By how much does the column shrink when a 5000- kg truck is on it?
Andiswa Reply
hi
Abdulrahman
mola mass
Abdulrahman
hi
Asdesaw
what exactly is a transverse wave
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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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