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The maximum buoyant force is the weight of this much water, or

F B = w w = m w g = 1.00 × 10 8 kg 9.80 m/s 2 = 9.80 × 10 8 N.


The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.

Making connections: take-home investigation

A piece of household aluminum foil is 0.016 mm thick. Use a piece of foil that measures 10 cm by 15 cm. (a) What is the mass of this amount of foil? (b) If the foil is folded to give it four sides, and paper clips or washers are added to this “boat,” what shape of the boat would allow it to hold the most “cargo” when placed in water? Test your prediction.

Density and archimedes’ principle

Density plays a crucial role in Archimedes’ principle. The average density of an object is what ultimately determines whether it floats. If its average density is less than that of the surrounding fluid, it will float. This is because the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink.

The extent to which a floating object is submerged depends on how the object’s density is related to that of the fluid. In [link] , for example, the unloaded ship has a lower density and less of it is submerged compared with the same ship loaded. We can derive a quantitative expression for the fraction submerged by considering density. The fraction submerged is the ratio of the volume submerged to the volume of the object, or

fraction submerged = V sub V obj = V fl V obj . size 12{ { {V rSub { size 8{"sub"} } } over {V rSub { size 8{"obj"} } } } = { {V rSub { size 8{"fl"} } } over {V rSub { size 8{"obj"} } } } } {}

The volume submerged equals the volume of fluid displaced, which we call V fl size 12{V rSub { size 8{"fl"} } } {} . Now we can obtain the relationship between the densities by substituting ρ = m V size 12{ρ= { {m} over {V} } } {} into the expression. This gives

V fl V obj = m fl / ρ fl m obj / ρ ¯ obj ,

where ρ ¯ obj size 12{ { bar {ρ}} rSub { size 8{"obj"} } } {} is the average density of the object and ρ fl size 12{ρ rSub { size 8{"fl"} } } {} is the density of the fluid. Since the object floats, its mass and that of the displaced fluid are equal, and so they cancel from the equation, leaving

fraction submerged = ρ ¯ obj ρ fl . size 12{"fraction"`"submerged"= { { { bar {ρ}} rSub { size 8{"obj"} } } over {ρ rSub { size 8{"fl"} } } } } {}

Two cargo ships. One is floating higher in the water than the other.
An unloaded ship (a) floats higher in the water than a loaded ship (b).

We use this last relationship to measure densities. This is done by measuring the fraction of a floating object that is submerged—for example, with a hydrometer. It is useful to define the ratio of the density of an object to a fluid (usually water) as specific gravity    :

specific gravity = ρ ¯ ρ w , size 12{"specific"`"gravity"= { {ρ} over {ρ rSub { size 8{w} } } } } {}

where ρ ¯ size 12{ρ} {} is the average density of the object or substance and ρ w size 12{ρ rSub { size 8{w} } } {} is the density of water at 4.00°C. Specific gravity is dimensionless, independent of whatever units are used for ρ size 12{ρ} {} . If an object floats, its specific gravity is less than one. If it sinks, its specific gravity is greater than one. Moreover, the fraction of a floating object that is submerged equals its specific gravity. If an object’s specific gravity is exactly 1, then it will remain suspended in the fluid, neither sinking nor floating. Scuba divers try to obtain this state so that they can hover in the water. We measure the specific gravity of fluids, such as battery acid, radiator fluid, and urine, as an indicator of their condition. One device for measuring specific gravity is shown in [link] .

Questions & Answers

Calculate the Newton's the weight of a 2.5 Kilogram of melon. What is its weight in pound?
Rialyn Reply
calculate the tension of the cable when a buoy with 0.5m and mass of 20kg
Iga Reply
what is displacement
Nyamza Reply
it's the time rate of change of distance
what is the meaning of physics
Alausa Reply
to study objects in motion and how they interact or take part in the natural phenomenon of the universe.
an object that has a small mass and an object has a large mase have the same momentum which has high kinetic energy
Faith Reply
The with smaller mass
Since you said they have the same momentum.. So meaning that there is more like an inverse proportionality in the quantities used to find the momentum. We are told that the the is a larger mass and a smaller mass., so we can conclude that the smaller mass had higher velocity as compared to other one
Mathamaticaly correct
Mathmaticaly correct :)
I have proven it by using my own values
Larger mass=4g Smaller mass=2g Momentum of both=8 Meaning V for L =2 and V for S=4 Now find there kinetic energies using the data presented
grateful soul...thanks alot
2 stones are thrown vertically upward from the ground, one with 3 times the initial speed of the other. If the faster stone takes 10 s to return to the ground, how long will it take the slower stone to return? If the slower stone reaches a maximum height of H, how high will the faster stone go
Julliene Reply
how can i calculate it's height
is speed the same as velocity
Faith Reply
in a question i ought to find the momentum but was given just mass and speed
just multiply mass and speed then you have the magnitude of momentem
Consider speed to be velocity
it worked our . . thanks
Distinguish between semi conductor and extrinsic conductors
Okame Reply
Suppose that a grandfather clock is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you (@) shorten or (b) lengthen the pendulam to make the clock keep attain the preferred time?
Aj Reply
I think you shorten am not sure
shorten it, since that is practice able using the simple pendulum as experiment
it'll always give the results needed no need to adjust the length, it is always measured by the starting time and ending time by the clock
it's not in relation to other clocks
wat is d formular for newton's third principle
shorten the pendulum string because the difference in length affects the time of oscillation.if short , the time taken will be adjusted.but if long ,the time taken will be twice the previous cycle.
discuss under damped
Prince Reply
resistance of thermometer in relation to temperature
Ifeanyi Reply
that resistance is not measured yet, it may be probably in the next generation of scientists
Is fundamental quantities under physical quantities?
Igwe Reply
please I didn't not understand the concept of the physical therapy
John Reply
physiotherapy - it's a practice of exercising for healthy living.
what chapter is this?
this is not in this book, it's from other experiences.
am new in the group
please I have probably with calculate please can you please and help me out
John Reply
What is Boyce law
Sly Reply
Boyles law states that the volume of a fixed amount of gas is inversely proportional to pressure acting on that given gas if the temperature remains constant which is: V<k/p or V=k(1/p)
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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