The equivalent of the spring system of the Journal of Hubei Normal University under the action of constant force Wang Renhai Guo Kexin Xianning College Physics Department, 437005 points in Xianning, Hubei, can greatly simplify the calculation of such questions.
There is a large amount of motion in the physics about the motion of the spring oscillator system. The system is not isolated, it is often subjected to other forces, which makes the problem more complicated. How to simplify the calculation of such questions, occasionally involved in some reference books, but very incomplete, such as the basic physical analysis of the book involves the vertical suspension of the spring oscillator under the action of gravity. In this paper, the equivalent elastic force and the equivalent elastic potential energy are put forward for the case where the spring oscillator is subjected to a constant force along its longitudinal direction, and the calculation of such a problem is greatly simplified by applying this equivalent viewpoint.
1 Equivalent elastic force of the spring oscillator system under constant external force For the ideal spring oscillator placed horizontally, the linear coordinate is established along the longitudinal direction of the spring, and the 5 axis is the origin of the coordinate, located at the free extension of the spring, when the spring is subjected to a longitudinal direction For a constant force F, set its equilibrium position at 5 Y. There is obviously 2 which is the stiffness coefficient of the spring. In this case, when the spring vibrator vibrates at any position, the resultant force is 0 coordinate system. Obviously, the conclusion is that the spring oscillator is in the equilibrium position for the new sitting 4 mark origin, and the resultant force in the dimensional coordinate sink 2 is now form. 1 Although the formula contains an external force, it is formally identical to the linear restoring force of an isolated spring oscillator. This shape 2, the coordinate system can avoid external considerations, and consider this system as a new isolated spring vibration subsystem. According to this idea, the new spring vibration subsystem can be called the equivalent spring vibration subsystem of the original spring oscillator, and the combined force = equivalent to the elastic force under the equivalent spring vibration subsystem, of course, can also be called the original spring oscillator The equivalent elastic force of the system.
2 The equivalent elastic potential energy of the spring oscillator system under constant external force is a brief aspect of the discussion of the spring oscillator subsystem. For an isolated spring oscillator, the elastic potential energy of the coordinate system is The vibration of the vibrator from the mountain is 0, the potential energy is zero. It seems that the corpse 1 is subjected to the vibration of the spring vibration under the action of the external force. The corresponding potential energy form under the equivalent elastic force must be the form and the isolated spring. The potential energy form of the vibrator is the same, but its physical meaning is different. In terms of the balance position of the vibrator under the action of constant force, the potential energy is zero. On the other hand, the potential energy of the wooden body of the 振 spring oscillator is included in the equation, and the energy corresponding to the constant force work is also included. It is the total energy of the system, and is not the elastic potential energy in the true sense. Therefore, this energy is named as the equivalent potential energy of the original spring oscillator subsystem. The following is discussed in detail below.
First. For the training of the constant force in the spring system 1, it clearly meets the record of conservative power. So the spring movement is immortal! In the middle, the work done by it corresponds to the negative pit of the potential energy increment. In the six coordinates, it is set as the potential energy zero point. When the system is located in a pleasant place, the potential energy corresponding to the constant force factory is the child's time, bomb, 1 The bullets are broken, and = the potential energy is zero, then the elastic potential energy at 1 arbitrary position is 2 = female 2 female left knot. The total energy of the system is the result of this and the conclusions. The clothing is in the form of elastic potential energy in the isolated yellow-vibration subsystem in the coordinate system. From energy, so = + cut 2 can only be called equivalent elastic potential energy.
The face was deduced by Leding to see more clearly. =+ to the total energy of the system, rather than the elastic potential of the elastic yellow vibration subsystem. 3 Conclusion When analyzing the missile and the vibration subsystem is affected by the force of the force along its longitudinal direction, the bamboo can first determine that the system is subjected to constant force. The new position is balanced, and the coordinate system is established with reference to the equilibrium position, and then the equivalent elastic force is used according to the effect of constant force; It is turned into an isolated projectile yellow vibration subsystem, and according to the dynamics of the isolated bomb Xie Chen production system. This will simplify the NPC's calculations that must be emphasized in terms of equivalent potential energy; points must be disciplined at new equilibrium levels.
4 Apply the example, the quality is 1 and the fertilizer, the stiffness coefficient of the spring is, ask how much pressure is needed on the 4th board, so that when the force stops, it can make 4 jump when it jumps up. Was brought up.
This will be more troublesome if the traditional solution is used. During the whole movement of the system, the spring is always subjected to the constant pressure 〃1 of the slab, which satisfies the conditions analyzed above, so that an equivalent viewpoint can be used for solving.
In 3, the vertical coordinate line sinking axis is established with the position where the upper end of the spring is at the balance as the coordinate origin, and the upper end coordinate of the spring is raised when the X X is not added, then the x is added to the external force. When the factory is compressed, the single spring is compressed everywhere. According to the equivalent elastic force, when the external force factory is cancelled, the system vibrates in the vertical direction. Since only the equivalent elastic force works, the mechanical energy is conserved. If you can lift the 2, you must jump to the highest point of 12, and the kinetic energy is zero. Therefore, according to the conservation of mechanical energy, the actual elastic force of the spring acting on the claw 2 is 1210. At that time, m2 will be lifted. (1) When the type 23 is substituted into (4) and +m2g is obtained, the claw 2 is just lifted.
The solution here is much simpler than the traditional method.
1 Ji Yaping, Yu Lizhen. Basic physics analysis. Fujian Fujian Science and Technology Press, 1993 2 Qi Anshen, Du Yuying. General physics tutorial. Beijing Higher Education; Edition Society, 1997 3 Zhou Yibai. Theoretical mechanics tutorial. Beijing Higher Education Press, 986 4 Ma Wenwei. physics. Beijing Higher Education; Edition Society, 1999
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