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apparent weight loss = weight of fluid displaced

or

apparent mass loss = mass of fluid displaced.

The next example illustrates the use of this technique.

Calculating density: is the coin authentic?

The mass of an ancient Greek coin is determined in air to be 8.630 g. When the coin is submerged in water as shown in [link] , its apparent mass is 7.800 g. Calculate its density, given that water has a density of 1 . 000 g/cm 3 size 12{1 "." "000"`"g/cm" rSup { size 8{3} } } {} and that effects caused by the wire suspending the coin are negligible.

Strategy

To calculate the coin’s density, we need its mass (which is given) and its volume. The volume of the coin equals the volume of water displaced. The volume of water displaced V w size 12{V rSub { size 8{w} } } {} can be found by solving the equation for density ρ = m V size 12{ρ= { {m} over {V} } } {} for V size 12{V} {} .

Solution

The volume of water is V w = m w ρ w size 12{V rSub { size 8{w} } = { {m rSub { size 8{w} } } over {ρ rSub { size 8{w} } } } } {} where m w size 12{m rSub { size 8{w} } } {} is the mass of water displaced. As noted, the mass of the water displaced equals the apparent mass loss, which is m w = 8 . 630 g 7 . 800 g = 0 . 830 g size 12{m rSub { size 8{w} } =8 "." "630"`g - 7 "." "800"`g=0 "." "830"`g} {} . Thus the volume of water is V w = 0 . 830 g 1 . 000 g /cm 3 = 0 . 830 cm 3 size 12{V rSub { size 8{w} } = { {0 "." "830"`g} over {1 "." "000"`"g/cm" rSup { size 8{3} } } } =0 "." "830"`"cm" rSup { size 8{3} } } {} . This is also the volume of the coin, since it is completely submerged. We can now find the density of the coin using the definition of density:

ρ c = m c V c = 8 . 630 g 0 .830 c m 3 = 10 . 4 g /cm 3 . size 12{ρ rSub { size 8{c} } = { {m rSub { size 8{c} } } over {V rSub { size 8{c} } } } = { {8 "." "630"`g} over {0 "." "830"`"g/cm" rSup { size 8{3} } } } ="10" "." 4`"g/cm" rSup { size 8{3} } } {}

Discussion

You can see from [link] that this density is very close to that of pure silver, appropriate for this type of ancient coin. Most modern counterfeits are not pure silver.

Got questions? Get instant answers now!

This brings us back to Archimedes’ principle and how it came into being. As the story goes, the king of Syracuse gave Archimedes the task of determining whether the royal crown maker was supplying a crown of pure gold. The purity of gold is difficult to determine by color (it can be diluted with other metals and still look as yellow as pure gold), and other analytical techniques had not yet been conceived. Even ancient peoples, however, realized that the density of gold was greater than that of any other then-known substance. Archimedes purportedly agonized over his task and had his inspiration one day while at the public baths, pondering the support the water gave his body. He came up with his now-famous principle, saw how to apply it to determine density, and ran naked down the streets of Syracuse crying “Eureka!” (Greek for “I have found it”). Similar behavior can be observed in contemporary physicists from time to time!

Phet explorations: buoyancy

When will objects float and when will they sink? Learn how buoyancy works with blocks. Arrows show the applied forces, and you can modify the properties of the blocks and the fluid.

Buoyancy

Section summary

  • Buoyant force is the net upward force on any object in any fluid. If the buoyant force is greater than the object’s weight, the object will rise to the surface and float. If the buoyant force is less than the object’s weight, the object will sink. If the buoyant force equals the object’s weight, the object will remain suspended at that depth. The buoyant force is always present whether the object floats, sinks, or is suspended in a fluid.
  • Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.
  • Specific gravity is the ratio of the density of an object to a fluid (usually water).

Questions & Answers

what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
Ahmed
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Busayo
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
Anita
Yeah
yusuf
is not just a material
Neemat
it is the surface of a metal
Neemat
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
Awene
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
babels
pls what is mirage
babels
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
Deepika
what is the dimensional formula for torque
Otto Reply
L2MT-2
Jolly
same units of energy
Baber
what is same units of energy?
Baber
Nm
Sphere
Ws
Sphere
CV
Sphere
M L2 T -2
Dokku
it is like checking the dimension of force. which is ML2T-2
Busayo
ML2T-2
Joshua
M L2 T-2
Samuel
what is the significance of moment of inertia?
study
an object of mass 200g moves along a circular path of radius 0.5cm with a speed of 2m/s. calculate the angular velocity ii period iii frequency of the object
Faith Reply
w = 2/(0.005) period = PIE(0.005) f = 1/(PIE(0.005)) assuming uniform motion idk..
Georgie
w=2/(0.005)×100
isaac
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
Sphere
a=w.w.r=mv.v/r,w=mv/r=0.2×2/0.005=80rads-s
Mac
in the pole vaulter problem, how do they established that the mass is 5.00kg? where did that number come from?
-- Reply
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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