<< Chapter < Page Chapter >> Page >
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 see 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.

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!

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).

Conceptual questions

More force is required to pull the plug in a full bathtub than when it is empty. Does this contradict Archimedes’ principle? Explain your answer.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 3

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Concepts of physics' conversation and receive update notifications?

Ask