Pulse and retention

Содержание и основные понятия

The pulse of the body is equal to the mass product at the speed. In a closed system, the vector sum of the pulses remains constant.
GEF · Grade 9
PIF · Baseline
Interactive model
pulse
closed system
Reactive motion
impact
01
The physical picture
What happens and what boundaries the model has.
Main message
The pulse of the body is equal to the mass product at the speed. In a closed system, the vector sum of the pulses remains constant.
The pulse is a vector, so opposite directions are taken into account by signs or vector addition.
The external forces change the impulse of the system, and the internal forces redistribute it between the parts.
Reactive motion occurs when a part of the mass is removed at some speed.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
p
⃗
=
m
v
⃗
\vec p=m\vec v
p
​
=
m
v
body pulse
∑
p
⃗
до
=
∑
p
⃗
после
\sum\vec p_{\text{до}}=\sum\vec p_{\text{после}}
∑
p
​
up to
​
=
∑
p
​
after
​
Pulse retention
Review of the situation
When fired, the bullet gets the pulse forward, and the weapon gets the same impulse back.
04
Links and application
In the real world
When fired, the bullet gets the pulse forward, and the weapon gets the same impulse back.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Pulse and its preservation" through the model, not just through the formula.
Outcome 2
Clear and correct use of terms: pulse, closed system, jet motion.
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.
pulse
A vector value equal to the mass of the body at its speed.
closed system
A body system that can be neglected as part of the task.
Reactive motion
The movement of the body resulting from the separation of a part of the mass with a directed pulse from it.
impact
The movement of one part of the system to compensate for the change of impulse of the other part.
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.
p
⃗
=
m
v
⃗
\vec p=m\vec v
p
​
=
m
v
definition
Body pulse.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
⃗
∥
v
⃗
\vec p\parallel\vec v
p
​
∥
v
The pulse shall be applied as a vectorial measure of mechanical motion directed along the speed of the body.
p
∝
m
,
p
∝
v
p\propto m,\quad p\propto v
p
∝
m
,
p
∝
v
The measure chosen should increase equally with the increase in mass or speed in classical mechanics.
p
⃗
≡
m
v
⃗
\vec p\equiv m\vec v
p
​
≡
m
v
Equality is the definition of a classic impulse, not an autonomously proven nature.
Conditions:
Classic mechanics, constant mass and speed are much less than the speed of light; v is set in the selected inertial system.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
∑
p
⃗
до
=
∑
p
⃗
после
\sum\vec p_{\text{до}}=\sum\vec p_{\text{после}}
∑
p
​
up to
​
=
∑
p
​
after
​
model effect
Maintaining impulse.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
d
p
⃗
i
d
t
=
F
⃗
i
внеш
+
∑
j
F
⃗
j
i
\frac{d\vec p_i}{dt}=\vec F_i^{\,\text{внеш}}+\sum_j\vec F_{ji}
d
t
d
p
​
i
​
​
=
F
i
Outside
​
+
j
∑
​
F
ji
​
The change in impulses of each body causes the external and internal forces of the system.
∑
i
∑
j
F
⃗
j
i
=
0
\sum_i\sum_j\vec F_{ji}=0
i
∑
​
j
∑
​
F
ji
​
=
0
The internal forces are falling in pairs under Newton's third law.
∑
F
⃗
внеш
=
0
⇒
Δ
∑
p
⃗
=
0
⇒
∑
p
⃗
до
=
∑
p
⃗
после
\sum\vec F^{\,\text{внеш}}=0\Rightarrow\Delta\sum\vec p=0\Rightarrow\sum\vec p_{\text{до}}=\sum\vec p_{\text{после}}
∑
F
Outside
=
0
⇒
Δ
∑
p
​
=
0
⇒
∑
p
​
up to
​
=
∑
p
​
after
​
If the resulting external pulse is zero, the full pulse of the system does not change.
Conditions:
The closed system is either neglected by a small amount of external force in the time under consideration; the impulses are being generated vectorically in the same inertial system.
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 topic is that the impulse is a vector, so the opposite directions are taken into account by signs or vector addition.
How to Check the Mind
The external forces change the pulse of the system, the internal forces redistribute it between the parts. Then check the units, the direction of the vectors and the behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Pulse and retention
The pulse of the body is equal to the mass product at the speed. In a closed system, the vector sum of the pulses remains constant.
The pulse is a vector, so opposite directions are taken into account by signs or vector addition.
The external forces change the impulse of the system, and the internal forces redistribute it between the parts.
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.