System pulse

Содержание и основные понятия

The change in the pulse of the system is equal to that of the external forces. Internal forces are decreasing in pairs, so the impulse is retained for the closed system.
GEF · 10 grade
PIF · Baseline
Interactive model
centre of masses
force pulse
Reactive traction
closed system
01
The physical picture
What happens and what boundaries the model has.
Main message
The change in the pulse of the system is equal to that of the external forces. Internal forces are decreasing in pairs, so the impulse is retained for the closed system.
The centre of the mass of the closed system is moving evenly and flatly.
The short-term force is convenient to describe as an impulse.
Reactive motion does not require reliance on the external environment.
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.
Δ
p
⃗
=
F
⃗
Δ
t
\Delta\vec p=\vec F\,\Delta t
Δ
p
​
=
F
Δ
t
force pulse
M
V
⃗
цм
=
∑
i
p
⃗
i
M\vec V_{\mathrm{цм}}=\sum_i\vec p_i
M
V
zm
​
=
i
∑
​
p
​
i
​
System pulse
Review of the situation
The missile accelerates by venting back gas; the overall impulse of the rocket and jet is maintained.
04
Links and application
In the real world
The missile accelerates by venting back gas; the overall impulse of the rocket and jet is maintained.
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 "system impulse" theme through the model, not just the formula.
Outcome 2
Discretion and correct use of terms: centre of mass, force pulse, jet thrust.
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.
centre of masses
The point whose motion describes the progress of the system as a whole.
force pulse
A medium force for the duration of the action, equal to a change in the body pulse.
Reactive traction
Force generated by separation from the body of the flow of a substance with a directed pulse.
closed system
A body system that can be neglected as part of the task.
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.
Δ
p
⃗
=
F
⃗
Δ
t
\Delta\vec p=\vec F\,\Delta t
Δ
p
​
=
F
Δ
t
model effect
A pulse of strength.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
⃗
=
Δ
p
⃗
Δ
t
\vec F=\frac{\Delta\vec p}{\Delta t}
F
=
Δ
t
Δ
p
​
​
Newton's second law is recorded as the rate of impulse change.
F
⃗
Δ
t
=
Δ
p
⃗
\vec F\,\Delta t=\Delta\vec p
F
Δ
t
=
Δ
p
​
For constant force, equality is multiplied by the duration of its action.
J
⃗
=
F
⃗
Δ
t
\vec J=\vec F\,\Delta t
J
=
F
Δ
t
It's a time-made force that is called a force impulse equal to a body impulse change.
Conditions:
The force is constant in the module and direction at the interval Δt; the variable force requires an integral Δp = ¡F dt or mean force.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
M
V
⃗
цм
=
∑
i
p
⃗
i
M\vec V_{\mathrm{цм}}=\sum_i\vec p_i
M
V
zm
​
=
i
∑
​
p
​
i
​
model effect
The pulse of the system.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
R
⃗
цм
=
1
M
∑
i
m
i
r
⃗
i
,
M
=
∑
i
m
i
\vec R_{\mathrm{цм}}=\frac{1}{M}\sum_i m_i\vec r_i,\quad M=\sum_i m_i
R
zm
​
=
M
1
​
i
∑
​
m
i
​
r
i
​
,
M
=
i
∑
​
m
i
​
The position of the centre of masses shall be determined by the mass-weighted sum of the particle positions.
M
V
⃗
цм
=
∑
i
m
i
v
⃗
i
M\vec V_{\mathrm{цм}}=\sum_i m_i\vec v_i
M
V
zm
​
=
i
∑
​
m
i
​
v
i
​
For constant masses, the definition of the centre of masses is differentiated by time.
p
⃗
i
=
m
i
v
⃗
i
⇒
M
V
⃗
цм
=
∑
i
p
⃗
i
\vec p_i=m_i\vec v_i\quad\Rightarrow\quad M\vec V_{\mathrm{цм}}=\sum_i\vec p_i
p
​
i
​
=
m
i
​
v
i
​
⇒
M
V
zm
​
=
i
∑
​
p
​
i
​
Each component is the impulse of the particle concerned.
Conditions:
The constant mass particle system in the non-relativist mechanics; the speed and centre of the masses are set in the same counting 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
You can't put the formula on any situation just because it's a coincidence of letters. The key condition of this subject is that the center of the mass of the closed system moves evenly and bluntly.
How to Check the Mind
The short-term force is convenient to describe with the pulse. Then check the units, vector direction, and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
System pulse
The change in the pulse of the system is equal to that of the external forces. Internal forces are decreasing in pairs, so the impulse is retained for the closed system.
The centre of the mass of the closed system is moving evenly and flatly.
The short-term force is convenient to describe as an impulse.
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.