Mechanical energy

Содержание и основные понятия

The kinetic energy is traffic-related, potentially interaction- and position-related; in the conservative system, the amount is maintained.
GEF · Grade 9
PIF · Baseline
Interactive model
work
kinetic energy
Potential energy
Power
01
The physical picture
What happens and what boundaries the model has.
Main message
The kinetic energy is traffic-related, potentially interaction- and position-related; in the conservative system, the amount is maintained.
Work equals change in kinetic energy.
The force of gravity and the force of turgidity allow the introduction of potential energy.
The friction reduces mechanical energy, turning it into internal energy, but the full energy is stored.
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.
E
к
=
m
v
2
2
E_{\mathrm{к}}=\frac{mv^2}{2}
E
to
​
=
2
m
v
2
​
kinetic energy
E
п
=
m
g
h
E_{\mathrm{п}}=mgh
E
c/
​
=
m
g
h
Earth ' s Potential Energy
E
к
+
E
п
=
c
o
n
s
t
E_{\mathrm{к}}+E_{\mathrm{п}}=\mathrm{const}
E
to
​
+
E
c/
​
=
const
Mechanical energy storage
Review of the situation
If there is no resistance, the potential energy is reduced precisely by the amount of kinetic growth.
04
Links and application
In the real world
If there is no resistance, the potential energy is reduced precisely by the amount of kinetic growth.
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 "Mechanical energy" through the model, not just the formula.
Outcome 2
Clear and correctly use terms: work, kinetic energy, potential energy.
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.
work
The scalar measure of energy transmission by force when moving the point of its application.
kinetic energy
The power of mechanical motion is mv2/2 in classical mechanics.
Potential energy
Interface energy dependent on the mutual position of the bodies or parts of the system.
Power
Work or energy transferred per unit of time.
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.
E
к
=
m
v
2
2
E_{\mathrm{к}}=\frac{mv^2}{2}
E
to
​
=
2
m
v
2
​
model effect
kinetic energy.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
A
=
F
s
=
m
a
s
A=Fs=mas
A
=
F
s
=
ma
s
For the constant effect force along the movement, its work is equal to the product ma on the path.
v
2
−
v
0
2
=
2
a
s
⇒
a
s
=
v
2
−
v
0
2
2
v^2-v_0^2=2as\Rightarrow as=\frac{v^2-v_0^2}{2}
v
2
−
v
0
2
​
=
2
a
s
⇒
a
s
=
2
v
2
−
v
0
2
​
​
The speed and track connection in equal traffic makes it possible to exclude acceleration and the path.
A
=
m
v
2
2
−
m
v
0
2
2
=
Δ
E
к
A=\frac{mv^2}{2}-\frac{mv_0^2}{2}=\Delta E_{\mathrm{к}}
A
=
2
m
v
2
​
−
2
m
v
0
2
​
​
=
Δ
E
to
​
The value of mv2/2 is kinetic energy, because its change is equal to that of the resultant force.
Conditions:
Material point or moving body in classical mechanics; speed is much less than the speed of light.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
E
п
=
m
g
h
E_{\mathrm{п}}=mgh
E
c/
​
=
m
g
h
model effect
Potential energy at the ground.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
тяж
=
m
g
F_{\mathrm{тяж}}=mg
F
claim
​
=
m
g
Near the surface of the Earth, gravity is considered permanent by the module.
A
тяж
=
−
m
g
h
A_{\mathrm{тяж}}=-mgh
A
claim
​
=
−
m
g
h
When rising to height h, the force is directed opposite to displacement and does negative work.
Δ
E
п
=
−
A
тяж
=
m
g
h
\Delta E_{\mathrm{п}}=-A_{\mathrm{тяж}}=mgh
Δ
E
c/
​
=
−
A
claim
​
=
m
g
h
If zero is selected at h=0, the growth of the potential energy is mgh.
Conditions:
A homogeneous field of gravity in a small area near the Earth ' s surface; g continuously, h is measured from a clearly selected zero level.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
E
к
+
E
п
=
c
o
n
s
t
E_{\mathrm{к}}+E_{\mathrm{п}}=\mathrm{const}
E
to
​
+
E
c/
​
=
const
model effect
Maintaining mechanical energy.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
E
к
=
A
рез
\Delta E_{\mathrm{к}}=A_{\mathrm{рез}}
Δ
E
to
​
=
A
res.
​
According to the kinetic energy theory, the work of all forces is equal to the change of kinetic power.
A
пот
=
−
Δ
E
п
A_{\mathrm{пот}}=-\Delta E_{\mathrm{п}}
A
sweat.
​
=
−
Δ
E
c/
​
For gravity or other potential force, her work is equal to the loss of potential energy.
Δ
E
к
+
Δ
E
п
=
0
⇒
E
к
+
E
п
=
c
o
n
s
t
\Delta E_{\mathrm{к}}+\Delta E_{\mathrm{п}}=0\Rightarrow E_{\mathrm{к}}+E_{\mathrm{п}}=\mathrm{const}
Δ
E
to
​
+
Δ
E
c/
​
=
0
⇒
E
to
​
+
E
c/
​
=
const
If we don't do the unintelligent forces, reducing one kind of energy is exactly the same as increasing the other.
Conditions:
Locked mechanical system; only potential forces are operational or friction, resistance and external forces are operating at zero.
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 topic is that work equals change of kinetic energy.
How to Check the Mind
The force of gravity and the force of turgidity allow the introduction of potential energy. Then check the units, vector direction and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Mechanical energy
The kinetic energy is traffic-related, potentially interaction- and position-related; in the conservative system, the amount is maintained.
Work equals change in kinetic energy.
The force of gravity and the force of turgidity allow the introduction of potential energy.
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.