1. Use inequality (group) to find the focal length range of convex lens.
It is really difficult for junior high school students to find the focal length range of convex lens according to certain conditions. Solving this kind of problem with the knowledge of inequality (group) will make the problem difficult and easy.
For example, when a classmate places a lighted candle at a distance of 375px from the convex lens, he gets a reduced image on the screen, and when the candle is at a distance of 225px from the lens, he gets an enlarged image on the screen. Try to find the range of focal length of convex lens.
Analysis: According to the law of convex lens imaging, students are first required to find out the corresponding relationship between object distance and focal length from the given imaging properties, so that when the real image is enlarged, when the real image is reduced, the known conditions are substituted into the above relationship to obtain:
Solve the inequality group and get
Answer:
Second, use the proportional method to solve physical problems
Proportional method is a method to solve physical problems by using proportional formula. In solving problems, according to physical laws, formulas or how many proportions of some quantities are equal, the relationship between unknown quantity and known quantity is established by using proportional formula, and then the unknown quantity is calculated by using proportional properties. In many cases, the proportional method is very simple, as long as the units of specific quantities are the same, and there is no need to unify them into international units.
For example, in March 2006 1, China began to implement a new energy efficiency standard for color TVs, stipulating that color TVs with standby power higher than 9W cannot enter the market. Xiao Ming wants to know whether the color TV at home meets the new energy efficiency standards. He connected the 100W light bulb to the circuit alone, and observed that the electric energy meter turned five times at 1 min. Let this color TV set be connected to the circuit alone and be in standby state, and the watt-hour meter will turn twice in 5 minutes, thus judging that the standby power of this color TV set is _ _ _ _ _ W.
Analysis: This is a typical electrical calculation problem, which should be calculated as follows according to the routine:
w 1 = Pt = 100 w× 1×60s = 3.0× 104j =
Suppose the speed of the electric energy meter is n revolutions/kW h? Formulas can be listed:
In this way, we can solve it with mathematical knowledge: N=3000rev/
Then the power consumption of color TV standby for 5 minutes is:
P2 = =/= 0.008 =8W
From this, it can be judged that this color TV meets the new national standard.
But if we carefully analyze and study this topic, we will find that the calculation can be simplified if the proportional method is used.
The solution is as follows: We can set the standby power of color TV to
We can solve =8W in one step, and we can see the simplified process by using the proportional method. But when dealing with this, the students' mathematical foundation is very demanding.
Others are as follows: when the current through the electric heater is 0.5A, the heat released in time t is Q; If the current flowing through it increases to 1.5A, the heat released in the same time is _ _ _ _ _ _ _ _.
Analysis: This physics topic examines Joule's law, so if the current is 0.5A, all physical quantities are subscript 1, and when the current is 1.5A, the subscript is 2, then
Because in this problem, the electric heaters are the same, that is to say =, heating for the same time also means t 1=t2, then the ratio of the above two formulas leads to Q2=9Q 1.
Of course, the ratio also appears in physical topics such as density and speed, and interested students can look it up by themselves.
Third, the application of trigonometric functions
Trigonometric function is not used much in junior high school physics, but it is used more in senior high school. The solution process is roughly as follows: reading the meaning of the question → setting the angle to establish a triangle → carrying out triangle transformation → solving practical problems.
For example, as shown in the figure, when the vertical rod is slowly moved to the horizontal position by a force F whose direction is always horizontal, what is the magnitude of the force F in this process?
Analysis: this question first makes the arm of force, and then lists the equation from the lever balance condition. We take an arbitrary intermediate process and set the lever at an angle with the vertical dotted line. The length of the lever is l, the gravity of the lever itself is g,
Then we can list the equations from the mathematical knowledge:
Finally, we get the following results: F=
In this way, from the knowledge of trigonometric function, we can analyze and study that the change of output f is gradually increasing.
Fourthly, the mathematical idea of combining numbers and shapes is widely used in physics.
In physics, mathematical images are often used to express the relationship between physical phenomena and physical knowledge. For example, in the chapter of state change, the characteristics of crystal melting and liquid boiling in state change are expressed by temperature-time images. The images involved are crystalline (amorphous) melting images, water boiling images and so on. Image method has the unique advantages of intuition, image, simplicity and strong generalization ability. It can present physical scenes, physical processes and physical states to us in an intuitive way.
The general steps of solving problems by image method are as follows: (1) See clearly the physical quantities represented by the abscissa and ordinate in the image; (2) Find out the dividing value on the coordinate; (3) Clarify the physical meaning expressed by the image, and analyze, reason, judge and calculate by using the intersection coordinates, slope, intercept intersection and the area surrounded by the image and coordinates; (4) Calculate the data in the topic or make a judgment conclusion according to the image.
For example, Xiao Wang did the experiment of "Comparison of Thermal Insulation Properties of Two Materials". He took ① and ② two kinds of thermal insulation materials, two identical thermometers, two identical large glass beakers, a hot water with the same clock and initial temperature and the same quality, as well as thin iron wire, cardboard and scissors, and made two thermal insulation devices with the same appearance, one of which is shown in Figure (a). Then I began to do experiments in the same room at the same time. According to the data measured in the experiment, he drew the image of "the relationship between water temperature and time" as shown in figure (b). During the experiment, the room temperature remained unchanged. Please answer:
(1)① and ② Which material has good thermal insulation performance? Answer: _ _ _ _ _ _ _ _ _ _ (choose ① or ②).
(2) For water in the same thermal insulation material, the heat released within 65438±00min to 20min _ _ _ _ _ the heat released within 20 min to 30min (please fill in "greater than", "equal to" or "less than").
(3) During the whole experiment, ① the heat released by water in thermal insulation material is _ _ _ _ _ _ _ _ _; ② Heat released by water in thermal insulation materials (select "greater than", "equal to" or "less than").
Analysis: As shown in the figure, we first observe that the abscissa and ordinate represent time and temperature respectively according to the above steps, and then observe the dividing value to see clearly the requirements of the topic. You need to see that the time scale value is 10 minute, 5 minutes, and the temperature is 10℃, which is helpful for the second question. The coincidence of the starting point and the ending point of the final image illustrates the intention of the third question.
Answer: (1) ①; (2) greater than; (3) equal to.
For example: A and B have the same mass, and the distance and time images in the driving process are as shown in the figure, then the following statement is correct ().
A. During driving, the kinetic energy of the two cars is always equal.
B. During driving, both A and B are acted by balancing force.
C. If they are heading east on the same straight highway, take car B as the reference and car A is heading west;
D. If the resistance of two cars is equal during driving, the power ratio of car A and car B is 4: 9.
The answer to this question: B.
In fact, a large number of numbers and shapes are involved in physics, density, speed of motion and optics.
5. The ability of reverse thinking plays an indelible role in physics.
Reverse thinking is a method of reverse thinking. There are many specific application methods, such as logic inversion, sequence inversion and path inversion. Using reverse thinking, we can explore the reasons for the development of things from the results of the development of things, consider problems in reverse, and consider problems against the time sequence of the development of things. Using reverse thinking, we can break through the conventional way of thinking, analyze problems skillfully, solve problems concisely and achieve unexpected results. For example, an object that satisfies two force equilibrium conditions must also be in equilibrium, and conversely, an object in equilibrium must also satisfy two force equilibrium conditions. Another example: electricity produces magnetism, magnetism can also produce electricity, and the optical path is reversible. Are applicable to this mode of thinking.
Physics is a high-level and high-grade culture and an important part of modern civilization. To learn well, we should learn to form scientific thinking methods, flexible skills, independent innovation consciousness, physical tricks to improve efficiency and so on. Through the training of physical thinking methods, people can observe the scientific spirit and realistic style of predecessors in various ways. And all this is inseparable from the cornerstone of mathematics. Perhaps this is the reason why we didn't start studying physics until the eighth grade.
Finally, I wish the students early academic success!