Archimedic Power

Содержание и основные понятия

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Alterna · physics · 3.4
Archimedic Power
Repulsive force, swimming bodies, vessels
"Eureka!" cried Archimedes, jumping out of the bathtub. He realized that the body in the water was losing part of the weight. Why did the steel ship not sink and the nail sink?
GEF · Grade 7
PIF · Baseline
01
Operation of liquid on body
Why does the body look easier in the water?
Repulsive force
The fluid presses the body from all directions, but the pressure from the bottom is greater than the top (because the depth is greater).
Pulse force
which is directed upwards.
That's why it's easier to hold a heavy rock in the water, part of its weight is "compensated" by a push-out force.
02
Archimedic Power
The force that pulls the body out of the liquid.
Archimedes Act
A body drowned in a liquid (or gas) is subject to a force of force that is equal to the weight of the liquid displaced by that body.
F
A
= ρ
cf
· g · V
pogre
where
cf
— density of liquid, V
pogre
- the volume of the body's drowned.
🎉
Archimedic Power — Immersion
IV-029 · F = gV, graph F(h)
Deep:
50
%
Liquid:
03
Swimming bodies
When it drowns, when it swims, when you're hanging in the thick?
Navigational conditions
ρ
Body
> ρ
Liquids
The body is drowning.
ρ
Body
= ρ
Liquids
The body swims inside the liquid.
ρ
Body
< ρ
Liquids
The body swims on the surface
Spray of drowned part: V
pogre
/V
Body
= ρ
Body
/ρ
Liquids
🎉
Swimming Bodies — Density
IV-030 · liquid selection + body density
Liquid:
Body density:
700
kg/m3
That's curious: the legend of archimedes.
King Gierón asked Archimedes to see if the jeweler had put silver in the golden crown, and in taking the bath, he saw the water spilling over the edge, and realized that the amount of water displaced was equal to the volume of the body drowned. "Eureka!" (Found!) he screamed and ran around the streets of Syracuse naked.
04
Navigation of ships.
Why don't steel ships sink?
Navigation
Steel (\18,000 kg/m3) is heavier than water — a whole piece of steel is drowning, but the ship is
a floor body
The average density of the ship < ~ water.
Waterline
is the line on the shell indicating the maximum draught at full load.
Water displacement
is the mass of water displaced by the vessel when diving to the waterline.
🚢
Water displacement and precipitation (animation)
IV-031 · Ship is pumped on waves + smooth loading + smoke from pipe
Mass of cargo:
0
t
Air
A ball filled with
Light gas
(helium, hydrogen) or warm air, it takes off because its average density is less than the density of the air.
A
= ρ
Hello.
·g·V.
Air balloons and airships are aircraft ships.
C
What needs to be understood
Outcome 1
Explain the physical meaning of "Archimedian Power" through a model, not just a formula.
Outcome 2
Distinguish and correctly use terms: archimedes power, swimming, displaced volume.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Archimedes Power
The force applying to the liquid or gas side equal to the weight of the displaced medium.
navigation
Equivalence or movement of the body in a liquid or gas under the joint application of gravity and force.
displaced volume
A large part of a body that's drowned in a liquid or gas equal to the volume of a displaced environment.
Water displacement
Mass or volume of liquid displaced by the floating body.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
F
A
=
ρ
ср
g
V
выт
F_{\mathrm{A}}=\rho_{\text{ср}}gV_{\text{выт}}
F
A
​
=
ρ
cf
​
g
V
out
​
model effect
Archimedic strength.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
низ
−
p
верх
=
ρ
ср
g
Δ
h
p_{\text{низ}}-p_{\text{верх}}=\rho_{\text{ср}}g\Delta h
p
bottom
​
−
p
top
​
=
ρ
cf
​
g
Δ
h
The hydrostatic pressure on the lower parts of the body is greater than on the upper surface.
F
A
=
m
выт
g
F_{\mathrm{A}}=m_{\text{выт}}g
F
A
​
=
m
out
​
g
The sum of the pressure forces is directed upwards and equals the weight of the medium occupied by the displaced volume.
m
выт
=
ρ
ср
V
выт
⇒
F
A
=
ρ
ср
g
V
выт
m_{\text{выт}}=\rho_{\text{ср}}V_{\text{выт}}\Rightarrow F_{\mathrm{A}}=\rho_{\text{ср}}gV_{\text{выт}}
m
out
​
=
ρ
cf
​
V
out
​
⇒
F
A
​
=
ρ
cf
​
g
V
out
​
The mass of displaced liquid or gas is determined by the density of the environment and the volume displaced.
Conditions:
The displaced volume V is in one standing homogeneous liquid or gas density , g constant, surface tension is insignificant, and for several media, their deposits are added together.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this subject is that the body is drowning.
How to Check the Mind
Body = fluids ~ body swims inside the liquid then check the units, direction of vectors and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Archimedic Power
"Eureka!" cried Archimedes, jumping out of the bathtub. He realized that the body in the water was losing part of the weight. Why did the steel ship not sink and the nail sink?
Body > liquidity ♪ body drowning
Body = fluids ~ body swims inside liquid
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.