Collisions

Содержание и основные понятия

During a short collision, the internal forces are large, so the impulse of the system can often be considered to be still, and the kinetic energy is preserved only when the impact is steady.
GEF · Grade 9
PIF · Baseline
Interactive model
Collision
Pulmonary shock
non-resilient impact
distortion
01
The physical picture
What happens and what boundaries the model has.
Main message
During a short collision, the internal forces are large, so the impulse of the system can often be considered to be still, and the kinetic energy is preserved only when the impact is steady.
When the bodies are completely intact, they move together after the collision.
In the case of a pulmonary shock, both impulse and kinetic energy are preserved.
Deformation, heating and sound shall be obtained from part of the reference mechanical energy.
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.
m
1
v
⃗
1
+
m
2
v
⃗
2
=
(
m
1
+
m
2
)
u
⃗
m_1\vec v_1+m_2\vec v_2=(m_1+m_2)\vec u
m
1
​
v
1
​
+
m
2
​
v
2
​
=
(
m
1
​
+
m
2
​
)
u
non-resilient impact
Δ
E
к
≤
0
\Delta E_{\mathrm{к}}\le 0
Δ
E
to
​
≤
0
kinetic energy losses
Review of the situation
The two coupled wagons after the impact have a total speed found from the total pulse retention.
04
Links and application
In the real world
The two coupled wagons after the impact have a total speed found from the total pulse retention.
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 "Clashes" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use terms: collision, tremor impact, non-resilient impact.
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.
Collision
The short-term interaction of the bodies, which significantly changes their impulses.
Pulmonary shock
A collision that preserves both the impulse and the kinetic energy of the closed system.
non-resilient impact
A collision in which the kinetic energy of the system is not preserved, although the impulse of the closed system is maintained.
distortion
Change in shape or body size due to external influences.
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.
m
1
v
⃗
1
+
m
2
v
⃗
2
=
(
m
1
+
m
2
)
u
⃗
m_1\vec v_1+m_2\vec v_2=(m_1+m_2)\vec u
m
1
​
v
1
​
+
m
2
​
v
2
​
=
(
m
1
​
+
m
2
​
)
u
model effect
Non-resilient blow.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
⃗
до
=
m
1
v
⃗
1
+
m
2
v
⃗
2
\vec p_{\text{до}}=m_1\vec v_1+m_2\vec v_2
p
​
up to
​
=
m
1
​
v
1
​
+
m
2
​
v
2
​
Before the impact, the full pulse is equal to the vector sum of the pulses of two bodies.
v
⃗
1
′
=
v
⃗
2
′
=
u
⃗
\vec v_1'=\vec v_2'=\vec u
v
1
′
​
=
v
2
′
​
=
u
In the event of a totally non-resilient impact, the bodies are coupled and then moved at the same speed after the impact.
m
1
v
⃗
1
+
m
2
v
⃗
2
=
(
m
1
+
m
2
)
u
⃗
m_1\vec v_1+m_2\vec v_2=(m_1+m_2)\vec u
m
1
​
v
1
​
+
m
2
​
v
2
​
=
(
m
1
​
+
m
2
​
)
u
From the pulse, the pulse is compared to the pulse of the unit body after it has been struck.
Conditions:
A totally non-resilient short-term shock; external impulse during a collision can be neglected, speed taken into account direction.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
Δ
E
к
≤
0
\Delta E_{\mathrm{к}}\le 0
Δ
E
to
​
≤
0
model effect
Loss of kinetic energy.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
E
к
,
до
+
U
до
=
E
к
,
после
+
U
после
+
E
звук
+
⋯
E_{\mathrm{к,до}}+U_{\mathrm{до}}=E_{\mathrm{к,после}}+U_{\mathrm{после}}+E_{\mathrm{звук}}+\cdots
E
to
,
up to
​
+
U
up to
​
=
E
to
,
after
​
+
U
after
​
+
E
sound
​
+
⋯
The complete energy balance takes into account both pre- and post-crash domestic energy.
Δ
U
=
U
после
−
U
до
≥
0
\Delta U=U_{\mathrm{после}}-U_{\mathrm{до}}\ge0
Δ
U
=
U
after
​
−
U
up to
​
≥
0
In a common non-resilient collision, internal energy is increased by deformation and heating.
Δ
E
к
=
−
(
Δ
U
+
E
звук
+
⋯
)
≤
0
\Delta E_{\mathrm{к}}=-\left(\Delta U+E_{\mathrm{звук}}+\cdots\right)\le0
Δ
E
to
​
=
−
(
Δ
U
+
E
sound
​
+
⋯
)
≤
0
Without release of pre-supplied energy, the reduction of kinetic energy is equal to energy that has changed into other forms.
Conditions:
Isolated collision without the release of stored internal or chemical energy; ΔE_K is defined as energy after minus energy before.
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 that when the bodies are completely unresilient, they move together after a collision.
How to Check the Mind
At the silicon impact, both the pulse and kinetic energy are stored. Then check the units, vector direction, and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Collisions
During a short collision, the internal forces are large, so the impulse of the system can often be considered to be still, and the kinetic energy is preserved only when the impact is steady.
When the bodies are completely intact, they move together after the collision.
In the case of a pulmonary shock, both impulse and kinetic energy are preserved.
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.