Laws, in addition to writing, also use equations, equations, etc.
Formulas, proportional formulas, trigonometric functions, trigonometric equations, etc. , you can also use.
To describe the corresponding image. Mathematics can not only be used as a calculation formula.
Through it, it is widely used to derive formulas, express relationships and describe rules.
Law, as well as its own logical function and abstract function to assist things.
The formation of rational concepts and laws. Master mathematical methods in physics,
It is one of the keys to learn physics well. This paper only discusses the extreme value problem,
Symbolic problems, mathematical images, etc. In mechanics, heat and electricity
This paper briefly discusses.
First, the positive and negative symbols in physics
Positive and negative in mathematics reflect the size of numbers, but in physics,
In physics, the physical meanings of positive and negative reactions are very different.
1, the positive and negative in the vector reflect the direction. On the same straight line
In fact, it is generally stipulated that a certain direction is a positive direction and a vector in the same direction as it.
The quantity is positive, otherwise it is negative, thus making vector operation a standard.
Quantity operation. For example, in linear motion, if the initial speed is chosen as V0,
If the direction is positive, the object will slow down when the acceleration is negative.
Exercise. For example, in the vertical throwing action, taking the throwing point as the origin,
The upper displacement is positive, the lower displacement is negative and the upward velocity is positive.
The downward velocity is negative, so the reciprocating motion can be regarded as linear motion.
Upward motion processing.
Example: 1, at the height of 10 m above the ground, vertically upward at a speed of 5 m/s.
Throw a thing, don't remember the resistance, how many seconds does it land?
[Analytical solution] Taking the throwing point as the origin, the upward direction is positive, so
V0=5m/s？ 0? 5. s=- 10m, and substitute it into the displacement formula s = v0 t+ 1/2at? 0? 5 yes
- 10=5t-5t？ 0? 5 find t=2 seconds.
2. Positive and negative can reflect the increase or decrease of an object's energy. Dadang
When the energy increases to a positive value, it means that the energy is increasing; When energy
When the increase is negative, it means that the energy is decreasing. For example, driven by
The law of energy shows that when the resultant force does positive work on an object, the object moves.
Can be increased; When an external force does negative work on an object, the kinetic energy of the object decreases.
Less. Another example is that in heat, we record heat absorption and work done on gas as
Integrity, on the contrary, heat release and external work record is negative.
3. In the representation of potential energy, plus or minus means the sum of potential energy.
The size compared with the standard point. For example, we regard the desktop as zero potential energy.
Point, then the potential energy of each point above the desktop is positive, and the desktop is
The potential energy at the bottom is negative everywhere. In this case, the positive and negative tables
Display size.
4. In optics, positive and negative mean virtual and real. convex lens
The focal length is positive and the lens focal length is negative; The image distance of the real image is positive,
The image distance of the virtual image is negative.
Second, define physical quantities by mathematical methods.
Physical quantities are divided into basic quantities and derived quantities.
Type, can be expressed in mathematical form. A large number of cans
Use the following mathematical method to define.
1, ratio definition method: it is to use the "ratio" of two physical quantities.
Define a new physical quantity. For example, it reflects the kind of substance.
Density of properties or characteristics (ρ=m/v), electric field intensity (E=F/q),
Conductor resistance (R=u/I) reflecting the nature or characteristics of an object, transport
Dynamic speed (v=s/t), power (P=w/t), etc.
2. Product definition method: two or more physical quantities are multiplied.
Define the product of new physical quantities. For example, work (w
= f s cos θ), momentum (p=mv), kinetic energy (Ek =mv? 0? 5/2)
Wait a minute.
3. Definition method of formula deformation: use the existing formula deformation.
Defining a new physical quantity is a method. For example, according to resistance
Law (R=ρl/s), Hooke's law (f=κx), friction law (f=μN),
Self-induced electromotive force (ε = Δ I/Δ T), and the resistivity ρ is obtained.
Number k, friction coefficient μ, self-inductance coefficient L.
4. Sum and difference definition method: that is, one is defined by the sum and difference of physical quantities.
A new physical quantity. For example, the increment of kinetic energy (Ek = Ek2
–ek1), momentum increment (δ p = p2-p 1), etc.
Third, the application of extreme value in physics
In physics, we often encounter extreme and maximum problems, sometimes
The relationship between quadratic equations in one variable is sometimes triangular.
Extreme value, etc. The characteristics of solving such problems: on the basis of physical mechanism,
The key to solving the problem depends on mathematical means and methods, with the help of mathematics
Skills and skills.
Example 2: A and B cars are driving in the same direction. When t=0,
The two cars are just in phase, and their displacement changes with time T.
Especially: SA =10t; S b =2t+t？ 0? 5. At what moment, a car?
Ahead, the two cars are farthest apart?
[resolution] the distance between the two cars is:
δ S = S A-S B = 10t -(2t+t？ 0? 5)=-t？ 0? 5+8 tons
According to the properties of quadratic function, when x=-b/2a, δ s has
Maximum value, δ smax = (4ac-b? 0? 5)/4a, that is, when t=4s,
δSmax = 16m
[Note] The changing law of physical quantities can be used in many occasions.
Quadratic function y=ax? 0? 5+bx+c, according to the properties of quadratic function
Mass: when x=-b/2a, y has an extreme value, and the extreme value y=(4ac-b? 0? 5)/4a, when
A>0 has a minimum value, and when
Example 3. Assign q0 to two particles with a distance of r, so that
It becomes two charged bodies q 1 and q2, so how can electricity be distributed?
When is the coulomb force between two charged bodies maximum?
[Analytical solution] The coulomb force between two charged bodies is
F=kq 1q2/r？ 0? 5 q 1+q2=q0 is a certain value according to the meaning of the question, so when
When q 1=q2=q0/2, q 1q2 has a maximum, that is, F has a maximum.
Value. When the current is evenly distributed between two particles
Coulomb force is the largest, and the maximum value Fmax=Kq0? 0? 5/4r？ 0? 5.
Fourth, the application of images in physics
Images can directly reflect the interdependence of physical quantities.
Lai relation vividly expresses the laws of physics. Using images to solve problems,
It is good for me to make some complicated problems simple and clear.
It is of great benefit to students' ability to analyze and solve problems.
To sum up, the application of mathematical solutions in physics.
There are many kinds, and the same physical process can use two or two.
The key to solve the above method is to combine physical meaning with mathematical formula.
Only by combining the methods skillfully can we achieve better results. pass by
Based on the diversity and complexity of things and the two foundations of physics and mathematics.
The interpenetration and intersection between disciplines. Therefore, we should pay attention to it in our study.
Use relevant mathematical knowledge to solve physical problems, so as to cultivate yourself.
Correctly analyze the physical process and use mathematical tools to solve physical problems.
Ability.
Free space to cross activities with teachers, allowing theft.
It is allowed to whisper in private and ask teachers and classmates for help. Because we
It is often found that some students have a rich imagination.
Rich, but poor hands-on ability; Some students do well, but
Narrow thinking, if we combine the two organically and learn from each other's strengths,
It is the best combination. Even if the two levels are equal, they are harmonious.
You can also get inspiration from the works. The so-called "threesome, there must be my teacher."
At the same time, some activities have themes and contents and need to collect a lot of materials.
Materials can be organized into groups to complete. Such as "flower arrangement" and "edition"
Creation such as "face design" and "face painting" can be grouped and combined.
Collecting materials: you prepare the flower paste, I prepare the flowers, and we will
Get up and finish a bunch of artistic flower arrangement; Try four people to design together.
Unique layout; Decorate each other with an interesting one.
In a pleasant atmosphere of cooperation and deep friendship.
In the atmosphere, eliminate the worries of grades and take the initiative to participate in learning happily.
Process, to bring students a pleasant aesthetic taste, so that every
Students all realize that collective wisdom is better than individual wisdom, so as to cultivate it.
Cultivate students' good moral character of unity, mutual assistance and cooperation. In this way,
The time of homework is relatively shortened, but the quality of homework is improved.
Why not?
Without the participation of teachers' minds, the classroom is like no rain.
Water in spring, dry and cold, lack of water; No educational practice
Participation, educational research will be like a pool of autumn water that is about to dry up.
Dull and lifeless. Combine the art of art education with the art of life.
Combining two into one will be the accomplishment of every art teacher in the 2 1 century.
The pursuit of life.