Conservation of momentum Conservation of mechanical energy Under what conditions can the kinetic ene

Conservation of momentum includes conservation of mechanical energy and conservation of kinetic energy! Conservation of mechanical energy is used in the presence of height differences; The kinetic energy theorem is a way to find the conservation of kinetic energy, which is generally used when an object has an initial velocity, an end velocity, and a mass (not necessarily all three, but two)... P.S

The change of mechanical energy should be considered when the kinetic energy theorem is used, and the commonly used formula is 1 2mv 2-1 2mv0 2=-mgh (positive and negative do not affect the result, a negative sign on both sides can be ignored, and one on each side can be canceled).

Momentum theorem: The impulse force acting on an object is equal to the momentum of change of the object.

Expression: ft = mv mv'Target.

Kinetic energy theorem: The work done by the force is equal to the kinetic energy minus the initial kinetic energy.

Expression: f*s = early at the end of ek-ek.

Law of Conservation of Momentum: A system of external or external forces in which the total momentum of the system is zero and constant.

Protection Mechanical Energy: Mechanical energy is a general term for kinetic energy and potential energy, which are converted to each other only in the case of gravity (or spring force), kinetic energy of the working object (or elastic potential energy), gravitational potential energy, but the total mechanical energy remains the same.

Protection: nonsense energy, nature, energy is not conserved? ？

The conditions of adaptation look at the content of the theorem and think about too much to know.

What conforms to Newtonian mechanics is established in the macroscopic world. Not true in the microcosm.

Kinetic energy theorem. It is suitable for all moving objects and systems.

The amount of change in kinetic energy is equal to the work done by the combined external force.

The law of conservation of momentum.

Suitable for both before and after a collision;

The total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

The law of conservation of mechanical energy applies to smooth surfaces, or work done only by gravity and spring elasticity, and no work is done by other forces.

The kinetic energy theorem and the mechanical energy conservation theorem are the two most basic theorems in the view of energy, and they are also one of the most important theorems in high school physics. The following is the "Concept and Difference between the Theorem of Kinetic Energy and the Conservation of Mechanical Energy" compiled by me for your reference only, and you are welcome to read this article.

Kinetic energy theorem.

Kinetic energy is instantaneous and refers to the fact that the work done by a force on an object in a process is equal to the change in kinetic energy in this process. Kinetic energy is a state quantity with no negative values.

The combined external force (the sum of the external forces on the object, the final direction and magnitude of the resultant force of the object can be calculated by the orthogonal method according to the direction and the magnitude of the force) The work done on the object is equal to the change in the kinetic energy of the object. That is, the last kinetic energy minus the initial virtual kinetic energy.

The kinetic energy theorem generally only involves the beginning and end states of the object's motion, and the amount of change in the beginning and end states is obtained through the transformation of the energy when the work is done in the process of motion. However, the total energy follows the law of conservation of energy, and the transformation of energy includes changes in kinetic energy, potential energy, heat energy, light energy (not covered in high school), and other energy.

The theorem of conservation of mechanical energy

When a particle (or system of particles) moves in a potential field, the sum of its kinetic energy and potential energy remains unchanged; Or the sum of kinetic energy and potential energy does not change when an object moves in a gravitational field. Implicit in this statement is negligible changes in the kinetic energy of objects (such as the Earth) that generate the field of force. This can only be true in some special inertial frame of reference, such as the Earth frame of reference.

As shown in the diagram, if all resistance and energy loss are not taken into account, the rolling pendulum is only affected by gravity, in this ideal case, the gravitational potential energy and kinetic energy are converted into each other, while the mechanical energy remains unchanged, and the rolling pendulum will continue to move up and down.

The main differences between the kinetic energy theorem and the mechanical energy conservation theorem are:

1. Define different things: the kinetic energy theorem is to describe the relationship between the amount of kinetic energy change of the object and the work done by the resultant external force on the object, and the mechanical energy conservation theorem indicates that if the object is only subjected to gravity or elastic force to do the work, the kinetic energy and potential energy of the object are converted into each other, and the total mechanical energy of the object remains unchanged.

2. Different expressions: the expression of the kinetic energy theorem is: w=(1 2)mv1 -(1 2)mv0, and the expression of the mechanical energy conservation theorem is: ek0+ep0=ek1+ep1;

3. The scope of application is different: the kinetic energy theorem is applicable to work done under various circumstances, and the mechanical energy conservation theorem is only used when gravity or elastic force is used to do work.

1.Let's talk about the difference between the "conservation law" and the "theorem" in high school physics:

Of course, when selecting the research object, it can be an object or a system, but students should pay attention to the fact that it is much easier to use theorems when solving quantities about a single object and conservation laws when solving quantities about a system.

2.Conditions that distinguish the conservation of mechanical energy between machinery and momentum conservation:

The condition for the conservation of mechanical energy: from the perspective of work, the system only does work with gravity or elastic force (spring force only).That is to say, the conservation of mechanical energy only recognizes the work done by gravity and elastic force, regardless of the inside and outside of the system, the system can be subjected to other forces (such as frictional force), but as long as they do not do work, or the algebraic sum of the work done is zero, then the mechanical energy of the system is conserved.

Conditions for conservation of momentum: no force outside the system, or zero resultant force, or internal force much greater than external force, or the above conditions are met in a certain direction. That is, the conservation of momentum only recognizes the force external to the system, regardless of whether the force is experienced inside the system or not.

For example, in the bullet block model, one of our common basic models for taking heights, the mechanical energy is not conserved because of the frictional force (not because of the frictional force), but there is no other force outside the system, so the momentum is conserved. (Although there is friction inside the system, the conservation of momentum does not recognize it).

3.Distinguish between the momentum theorem and the kinetic energy theorem:

The momentum theorem is the accumulation of force in time, and it is the first choice when it is required to solve the force, time, velocity, momentum, change in momentum, and impulse in the problem.

The kinetic energy theorem is the spatial accumulation of force, which is the first choice when solving force, displacement, velocity, kinetic energy, change in kinetic energy, and work done in the problem.

4.Distinguish between the law of conservation of mechanical energy and the theorem of kinetic energy.

It can be said that the law of conservation of mechanical energy is a special expression of the kinetic energy theorem when only gravity and elastic force do work. For students who don't know when and which of the two should be used, the best thing to do is to just use the kinetic energy theorem.

5.Distinguish between conservation of mechanical energy and constant mechanical energy:

Conservation of mechanical energy is a dynamic process, conservation in change, that is to say, if you want to talk about conservation, you must first let it change.

Mechanical energy does not change because it is a static process, that is, it does not change. (No change is not the same as no change).

For example, if a car is driving at a constant speed on the horizontal plane, it can only be said that its mechanical energy is unchanged, but it cannot be said that its mechanical energy is conserved.

You should be so rational to understand the kinetic energy du theorem and the momentum theorem, in fact, they are both.

Derived from the kinematic gong dao, the former is the return energy, the unit is Joule, and the latter is the impulse, the unit is, or rather, the two represent different physical quantities.

First of all, the basic formula for doing work is w=fs, ox two has f=ma, and the kinematic formula is 2as=vt 2-v0 2, if we look at (vt 2-v0 2) as v 2, if we are solved by these four formulas, there is w=1 2mv 2, which is the kinetic energy theorem.

Looking at the momentum theorem again, from the basic formula i=ft, Niu Er has f=ma, and the kinematic formula at=v, after the solution, we get i=mv

And both kinetic energy and momentum are only used in the equations for m and v, so we often use them together to solve a lot of practical problems, and I say that, do you understand? It's all original, and if you don't understand, you can continue to ask

Difference Between Law of Conservation of Mechanical Energy and Law of Conservation of Momentum:

1.Conservation of momentum is vector conservation, and the conservation condition is from the point of view of force, i.e., not subject to external forces or the sum of external forces is zero. To determine whether momentum is conserved or not, the sum of external forces should be analyzed to see if it is zero;

The conservation of mechanical energy is the conservation of scalar quantities, and the conservation condition is from the perspective of work, that is, other forces do not do work except gravity and elastic force. To determine whether the mechanical energy of the system is conserved, the work done by the external force and the internal force should be analyzed to see whether only gravity and the elastic force of the system do the work.

It should also be noted that the sum of external forces being zero and the external force not doing work are two different concepts. Therefore, the momentum of the system is not necessarily conserved when the mechanical energy is conserved; Mechanical energy is also not necessarily conserved when momentum is conserved.

2.Apply the basic steps of the law of conservation of mechanical energy to solve the problem.

1) Select the object (object or system) according to the topic.

2) Clarify the motion process of the research object, analyze the force of the object in the process, find out the work done by each force, and judge whether the mechanical energy is conserved.

3) Appropriately select the zero potential surface to determine the mechanical energy of the beginning and end states of the research object in the process.

4) According to the different expressions of the law of conservation of mechanical energy, the equations are listed, and if the expression of increase (decrease) is selected, (3) it should be the increase or decrease of kinetic energy and potential energy in the process of determining the process or the increase or decrease of mechanical energy of each part of the process to solve the equation.

The law of conservation of mechanical energy is often combined with circular motion.

3.Characteristics of applying the law of conservation of momentum to solve problems.

1) The law of conservation of momentum has a wide range of applications, regardless of the nature of the interaction forces between objects; Regardless of the number of objects in the system; Whether it is a macroscopic low-speed moving object, or a microscopic high-speed moving particle; Regardless of whether they are in contact or not, the law of conservation of momentum applies as long as the resultant force on the system is 0.

2) Only need to know the state of the system before and after the change, and ignore the complex change process of each object in the system under the action of internal forces, and solve the problem simply and conveniently.

The comprehensive questions of the college entrance examination are not only the law of conservation of momentum in the mechanical process, but also the change of energy. It is often necessary to combine the kinetic energy theorem or the law of conservation of mechanical energy.

The Law of Conservation of Energy: Energy can neither be created or disappear out of thin air, it can only be transformed from one form of energy to another, or from one object to another, and the total amount of energy remains the same.

Applying the law of conservation of energy to remember two ideas:

1) The decrease in energy in one form must be equal to the increase in energy in other forms.

2) The decrease in the energy of one object must be equal to the increase in the energy of other objects.

The kinetic energy theorem calculates kinetic energy, which is the kinetic energy that an object has when it is moving, and a relatively stationary object has no kinetic energy, for example, if an object is moving in a straight line at a uniform speed, the mass is m, the velocity is v, so its kinetic energy is 1 2mv (squared).

The law of conservation of mechanical energy says that when an object has no external force to do work, the sum of kinetic energy and potential energy remains unchanged Kinetic energy is the one calculated by the kinetic energy theorem above Potential energy includes gravitational potential energy and elastic potential energy E machine = e potential + e motion.

1) The system is not subject to an external force or the net force of the external force on the system is zero. (2) Although the net force of the external force of the system is not zero, it is much smaller than the internal force of the system. (3) Although the resultant force of the external force on the system is not zero, when the component force in a certain direction is zero, the total momentum of the system remains unchanged in that direction - the partial momentum is conserved.

In the above three cases, the law of conservation of momentum is followed, that is, the sum of the momentum before the collision is equal to the sum of the momentum after the collision.

As long as the resultant external force is 0, then the mechanical energy is conserved, and if it is not acted upon by the external force, the momentum is conserved.

The kinetic energy theorem is that the work done by the combined external force is equal to the change in the kinetic energy of the object, which is often used to calculate the velocity, ek=1 2mv2

The law of conservation of mechanical energy means that the sum of gravitational potential energy and kinetic energy of an object remains constant, like a free fall, where mechanical energy is conserved.

Conservation of energy means that all kinds of energy do not disappear in vain and are not generated for no reason.