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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.

Do fluids exert buoyant forces in a “weightless” environment, such as in the space shuttle? Explain your answer.

Will the same ship float higher in salt water than in freshwater? Explain your answer.

Marbles dropped into a partially filled bathtub sink to the bottom. Part of their weight is supported by buoyant force, yet the downward force on the bottom of the tub increases by exactly the weight of the marbles. Explain why.

Problem exercises

What fraction of ice is submerged when it floats in freshwater, given the density of water at 0°C is very close to 1000 kg /m 3 size 12{"1000"`"kg/m" rSup { size 8{3} } } {} ?

91 . 7% size 12{"91" "." 7%} {}

Logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-diameter log that floats with 20.0% of its length above water?

Find the density of a fluid in which a hydrometer having a density of 0 . 750 g /mL size 12{0 "." "750"`"g/mL"} {} floats with 92.0% size 12{"92" "." 0%} {} of its volume submerged.

815 kg /m 3 size 12{"815"`"kg/m" rSup { size 8{3} } } {}

If your body has a density of 995 kg /m 3 size 12{"995"`"kg/m" rSup { size 8{3} } } {} , what fraction of you will be submerged when floating gently in: (a) Freshwater? (b) Salt water, which has a density of 1027 kg /m 3 size 12{"1027"`"kg/m" rSup { size 8{3} } } {} ?

Bird bones have air pockets in them to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. Suppose an ornithologist weighs a bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g size 12{3 "." "60"`g} {} (the bone is watertight). (a) What mass of water is displaced? (b) What is the volume of the bone? (c) What is its average density?

(a) 41.4 g

(b) 41 . 4 cm 3 size 12{"41" "." 4`"cm" rSup { size 8{3} } } {}

(c) 1 . 09 g /cm 3 size 12{1 "." "09"`"g/cm" rSup { size 8{3} } } {}

A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?

Archimedes’ principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) What mass of fluid does the iron displace? (b) What is the volume of iron, using its density as given in [link] (c) Calculate the fluid’s density and identify it.

(a) 39.5 g

(b) 50 cm 3 size 12{"50"`"cm" rSup { size 8{3} } } {}

(c) 0 . 79 g/cm 3 size 12{0 "." "79"`"g/cm" rSup { size 8{3} } } {}

It is ethyl alcohol.

In an immersion measurement of a woman’s density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L, is she able to float without treading water with her lungs filled with air?

Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in salt water if its body density is 1015 kg/m 3 size 12{"1015" `"kg/m" rSup { size 8{3} } } {} ?

8.21 N

(a) Calculate the buoyant force on a 2.00-L helium balloon. (b) Given the mass of the rubber in the balloon is 1.50 g, what is the net vertical force on the balloon if it is let go? You can neglect the volume of the rubber.

(a) What is the density of a woman who floats in freshwater with 4.00% of her volume above the surface? This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water (briefly). (b) What percent of her volume is above the surface when she floats in seawater?

(a) 960 kg/m 3 size 12{"960" `"kg/m" rSup { size 8{3} } } {}

(b) 6.34%

She indeed floats more in seawater.

A certain man has a mass of 80 kg and a density of 955 kg/m 3 size 12{"955" `"kg/m" rSup { size 8{3} } } {} (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?

A simple compass can be made by placing a small bar magnet on a cork floating in water. (a) What fraction of a plain cork will be submerged when floating in water? (b) If the cork has a mass of 10.0 g and a 20.0-g magnet is placed on it, what fraction of the cork will be submerged? (c) Will the bar magnet and cork float in ethyl alcohol?

(a) 0 . 24 size 12{0 "." "24"} {}

(b) 0 . 68 size 12{0 "." "68"} {}

(c) Yes, the cork will float because ρ obj < ρ ethyl alcohol ( 0 . 678 g/cm 3 < 0 . 79 g/cm 3 ) size 12{ρ rSub { size 8{"obj"} }<ρ rSub { size 8{"ethyl"`"alcohol"} } \( 0 "." "678"`"g/cm" rSup { size 8{3} }<0 "." "79"`"g/cm" rSup { size 8{3} } \) } {}

What fraction of an iron anchor’s weight will be supported by buoyant force when submerged in saltwater?

Scurrilous con artists have been known to represent gold-plated tungsten ingots as pure gold and sell them to the greedy at prices much below gold value but deservedly far above the cost of tungsten. With what accuracy must you be able to measure the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure gold?

The difference is 0.006%.

A twin-sized air mattress used for camping has dimensions of 100 cm by 200 cm by 15 cm when blown up. The weight of the mattress is 2 kg. How heavy a person could the air mattress hold if it is placed in freshwater?

Referring to [link] , prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes’ principle). You may assume that the buoyant force is F 2 F 1 size 12{F rSub { size 8{2} } - F rSub { size 8{1} } } {} and that the ends of the cylinder have equal areas A size 12{A} {} . Note that the volume of the cylinder (and that of the fluid it displaces) equals ( h 2 h 1 ) A size 12{ \( h rSub { size 8{2} } - h rSub { size 8{1} } \) A} {} .

F net = F 2 F 1 = P 2 A P 1 A = P 2 P 1 A size 12{F rSub { size 8{"net"} } =F rSub { size 8{2} } - F rSub { size 8{1} } =P rSub { size 8{2} } A - P rSub { size 8{1} } A= left (P rSub { size 8{2} } - P rSub { size 8{1} } right )A} {}

= h 2 ρ fl g h 1 ρ fl g A size 12{ {}= left (h rSub { size 8{2} } ρ rSub { size 8{"fl"} } g - h rSub { size 8{1} } ρ rSub { size 8{"fl"} } g right )A} {}

= h 2 h 1 ρ fl gA size 12{ {}= left (h rSub { size 8{2} } - h rSub { size 8{1} } right )ρ rSub { size 8{"fl"} } ital "gA"} {}

where ρ fl size 12{ρ rSub { size 8{"fl"} } } {} = density of fluid. Therefore,

F net = ( h 2 h 1 ) fl g = V fl ρ fl g = m fl g = w fl size 12{F rSub { size 8{"net"} } = \( h rSub { size 8{2} } - h rSub { size 8{1} } \) Aρ rSub { size 8{"fl"} } g=V rSub { size 8{"fl"} } ρ rSub { size 8{"fl"} } g=m rSub { size 8{"fl"} } g=w rSub { size 8{"fl"} } } {}

where is w fl size 12{w rSub { size 8{"fl"} } } {} the weight of the fluid displaced.

(a) A 75.0-kg man floats in freshwater with 3.00% of his volume above water when his lungs are empty, and 5.00% of his volume above water when his lungs are full. Calculate the volume of air he inhales—called his lung capacity—in liters. (b) Does this lung volume seem reasonable?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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
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Source:  OpenStax, Physics of the world around us. OpenStax CNX. May 21, 2015 Download for free at http://legacy.cnx.org/content/col11797/1.1
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