Force and traffic equations

Содержание и основные понятия

The problem of dynamics begins with the selection of the body and the system of counting, then depicts only the forces attached to the body, and records Newton's second law in projections.
GEF · 10 grade
PIF · Baseline
Interactive model
Force diagram
support leg reaction
tension
friction
related bodies
01
The physical picture
What happens and what boundaries the model has.
Main message
The problem of dynamics begins with the selection of the body and the system of counting, then depicts only the forces attached to the body, and records Newton's second law in projections.
The normal reaction is not always equal to mg and is determined by the motion condition.
The friction force of the rest shall be adjusted to the limit value.
The thread and the block create connections between the accelerations of the bodies, which must be taken into account with the force equations.
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.
∑
F
x
=
m
a
x
\sum F_x=ma_x
∑
F
x
​
=
m
a
x
​
projection of the second law
0
≤
F
тр
.
п
≤
μ
п
N
0\leq F_{\mathrm{тр.п}}\leq\mu_{\mathrm{п}}N
0
≤
F
t/
.
c/
​
≤
μ
c/
​
N
the friction of the rest
Review of the situation
On an inclined plane, it is convenient to direct the axis along the surface: then the gravity force is placed on mg sine α and mg cosine α.
04
Links and application
In the real world
On an inclined plane, it is convenient to direct the axis along the surface: then the gravity force is placed on mg sine α and mg cosine α.
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 "Powers and traffic equations" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use terms: force diagram, support response, tension.
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.
Force diagram
A pattern of the body chosen, with all the external forces attached to it and their directions.
support leg reaction
The force of turgency with which the support acts on the body in contact with it.
tension
The force of the turgidness with which the thread, cable or rod is drawn on the attached body.
friction
Communicating bodies that prevent their relative movement or formation.
related bodies
Bodies whose movements are limited by communication, such as an inexhaustible thread or a common support.
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.
∑
F
x
=
m
a
x
\sum F_x=ma_x
∑
F
x
​
=
m
a
x
​
model effect
The projection of the second law.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
∑
F
⃗
=
m
a
⃗
\sum\vec F=m\vec a
∑
F
=
m
a
Based on Newton's second law for a permanent mass material point.
(
∑
F
⃗
)
x
=
(
m
a
⃗
)
x
\left(\sum\vec F\right)_x=(m\vec a)_x
(
∑
F
)
x
​
=
(
m
a
)
x
​
Both parts of the vector equation shall be projected to the chosen x axis.
∑
F
x
=
m
a
x
\sum F_x=ma_x
∑
F
x
​
=
m
a
x
​
The projection of the sum is equal to the sum of the projections and the scalar mass is given as the projection mark.
Conditions:
Inertial counting system, body is modelled by a physical point with constant mass; the sum includes all external forces.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
0
≤
F
тр
.
п
≤
μ
п
N
0\leq F_{\mathrm{тр.п}}\leq\mu_{\mathrm{п}}N
0
≤
F
t/
.
c/
​
≤
μ
c/
​
N
empirical law
The friction of peace.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
тр
.
п
=
F
∥
F_{\mathrm{тр.п}}=F_{\parallel}
F
t/
.
c/
​
=
F
∥
​
While the body is resting, the frictional force is adjusted and balanced by the movement of the body to the tangential force.
F
тр
.
п
max
⁡
=
μ
п
N
F_{\mathrm{тр.п}}^{\max}=\mu_{\mathrm{п}}N
F
t/
.
c/
m
a
x
​
=
μ
c/
​
N
Experience shows that the maximum friction ratio of the normal response is close; the coefficient depends on the pair of surfaces.
F
тр
.
п
≤
μ
п
N
F_{\mathrm{тр.п}}\leq\mu_{\mathrm{п}}N
F
t/
.
c/
​
≤
μ
c/
​
N
The actual friction does not exceed the measured limit before slip.
Conditions:
Dry contact of macroscopic bodies without rolling; μp is considered permanent for these surfaces and conditions, and inequality only operates in rest mode.
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 formula cannot be transferred to any situation simply because the letters match. The key condition of this topic is that the normal reaction is not always equal to mg and determined by the condition of motion.
How to Check the Mind
The friction force of the rest shall be adjusted to the limit value. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Deformation and Yung module
In the case of slight permeation, the elongation . . = Δl/l0 is proportional to the mechanical voltage . F/S. The coefficient E = . / . is referred to as the Yung module. The law applies only in the area of turgidity: after exceeding the limit of tibia, the body does not return completely to the original form.
Σ
Conclusion on the topic
Force and traffic equations
The problem of dynamics begins with the selection of the body and the system of counting, then depicts only the forces attached to the body, and records Newton's second law in projections.
The normal reaction is not always equal to mg and is determined by the motion condition.
The friction force of the rest shall be adjusted to the limit value.
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.