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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.

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

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

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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.

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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%} {}

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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?

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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} } } {}

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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} } } {} ?

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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} } } {}

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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?

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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.

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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?

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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

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(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.

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(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.

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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?

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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"} } \( 0 "." "678"`"g/cm" rSup { size 8{3} }<0 "." "79"`"g/cm" rSup { size 8{3} } \) } {}

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

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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%.

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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?

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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.

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(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?

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Questions & Answers

derivative of first differential equation
Haruna Reply
why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
what Is linear momentum
Victoria Reply
why no diagrams
Blessing Reply
where
Fayyaz
Myanmar
Pyae
hi
Iroko
hello
Abdu
Describe an experiment to determine short half life
Tyson Reply
what is science
Kenedy Reply
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
there are seven basic type of wave radio waves, gyamma rays (nuclear energy), microwave,etc you can also search 🔍 on Google :-)
Shravasti
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
what is physics
Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
Magret Reply
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
fundamental quantities are, length , mass, time, current, luminous intensity, amount of substance, thermodynamic temperature.
Shravasti
fundamental quantities are quantities that are independent of others and cannot be define in terms of other quantities there is nothing like Qualities we have only fundamental quantities which includes; length,mass,time, electric current, luminous density, temperature, amount of substance etc
Gift
give examples of three dimensional frame of reference
Ekwunazor Reply
Universe
Noman
Yes the Universe itself
Astronomy
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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