Mass and density

Содержание и основные понятия

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Alterna · physics · 2.2
Mass and density
Body interaction, mass, density of substance
Why is the size of an iron cube equal to that of a tree? What is mass really -- and how is it related to inertia? Understand why bodies are drowning or swimming.
GEF · Grade 7
PIF · Baseline
01
Body interaction
In interaction, both bodies change speed.
What is interaction?
The bodies work on each other -- that's what they are.
interaction
Both bodies change their speed when they interact.
An example of this is a puppy kick, the stick slows down a little bit, the puck goes a little faster.
Innerity
Innerity
The larger the body's mass, the more inert it is, the harder it is to change its speed.
⚖
Body Interface — Mass Ratio
IV-014 · v₁/v₂ = m₂/m₁
m₁:
2
kg
m₂:
4
kg
02
Mass of body.
Mass is a measure of body inertia.
Mass
Mass
The bigger the mass, the harder it is to change the speed of the body.
Mass unit:
kg (kg)
.
Other units: 1 t = 1,000 kg, 1 g = 0.001 kg,1 mg = 0.00001 kg.
That's curious.
The standard of a kilogram is a cylinder of platino iridium alloy stored at the International Bureau of Measures and Weights in Paris, and since 2019, the kilograms have been determined through a permanent Planck.
03
Density
Why do the bodies of the same volume have different masses?
Density
Density
is a physical value equal to the mass of the body to its volume.
ρ = m / V
Unit:
kg/m3
Also used is g/cm3 (1 g/cc3 = 1000 kg/m3).
Table of carpentry (kg/m3)
Substance
, kg/m3
Substance
, kg/m3
Osmium
22600
Water
1000
Gold
19300
Ice
900
Lead
11300
Oil
900
Silver
10500
Alcohol
800
Copper
8900
Petrol
710
Steel
7800
Oak
700
Aluminium
2700
Traffic
240
⚖
Density calculator M/V
IV-015 · Calculation + comparison with water (tonet/float)
Mass m (kg):
Grouping V (m3):
04
Calculation of mass and volume by density
From the formula m/V is obtained m = V and M/V.
Three formulas
ρ = m/V
→
m = ρ · V
→
V = m/ρ
Example
Find the mass of the aluminium part of 0.5 m3. * = 2,700 kg/m3. m = 2700 x 0.5 = 1350 kg.
That's curious. Space objects.
The density of a neutron star is about 1,017 kg/m3. This means that a tea spoon of a neuron star substance would weigh about a billion tons on Earth.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the theme "mass and density" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use terms: mass, volume, density.
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.
Mass
Body inertia measure and source of gravitational interaction.
volume
The physical value of the part of the space occupied by the body.
density
The ratio of the mass of the homogeneous substance to the volume it holds.
Average density
The ratio of the total mass of the variable body to the total volume.
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.
ρ
=
m
V
\rho=\frac{m}{V}
ρ
=
V
m
​
definition
The density.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
m
∼
V
m\sim V
m
∼
V
For a homogeneous substance, the mass of the sample is proportional to its volume.
ρ
=
m
V
\rho=\frac{m}{V}
ρ
=
V
m
​
Density is introduced as the mass of a unit of volume; for this homogeneous substance the ratio is constant.
Conditions:
A homogeneous body or average density of a non-different body, V > 0; temperature and pressure shall be indicated if the volume is significantly affected.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
m
=
ρ
V
m=\rho V
m
=
ρ
V
model effect
Mass by density and volume.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
ρ
=
m
V
\rho=\frac{m}{V}
ρ
=
V
m
​
The density is equal to the mass of the unit of uniform matter.
ρ
V
=
m
\rho V=m
ρ
V
=
m
The multiplication by full volume add up the same mass of all units of volume.
m
=
ρ
V
m=\rho V
m
=
ρ
V
The mass of a homogeneous body is equal to the product of its density and volume.
Conditions:
Density is constant throughout the volume; for a dissimilar body, the density must be mean or the summation of parts is required.
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
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this topic is, why does the iron and the tree have the same weight? What is mass really -- and how does it relate to inertia? Understand why bodies drown or swim.
How to Check the Mind
The formula is only applicable after selecting the system and assumptions. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Mass and density
Why is the size of an iron cube equal to that of a tree? What is mass really -- and how is it related to inertia? Understand why bodies are drowning or swimming.
Why is the size of an iron cube equal to that of a tree? What is mass really -- and how is it related to inertia? Understand why bodies are drowning or swimming.
The formula is applicable only after the selection of the system and assumptions.
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.