Mechanical energy is conserved, so how can the energy be depleted

Converted into other forms of energy (e.g. heat, light, etc.).

The law of conservation of mechanical energy is expressed as follows: in the case of only gravity doing work, the kinetic energy and potential energy of the object are converted into each other, but the total amount of mechanical energy remains the same. This is the most common case of the law of conservation of mechanical energy (i.e., the case where only gravity does the work in the mutual conversion of gravitational potential energy and kinetic energy.

In fact, in the mutual conversion of gravitational potential energy and elastic potential energy with kinetic energy, only when gravity and the elastic force of the spring do work, the sum of the kinetic energy of the object and the potential energy of the system remains unchanged, and the mechanical energy of the system is conserved), which is also a special case of the more general law of conservation of energy.

The law of conservation of mechanical energy can be considered as the law of energy conversion and conservation in mechanics. Its condition is that the system only has gravity and elasticity to do work. In such a system, the total mechanical energy is constant despite the mutual conversion of kinetic energy and potential energy. Here we talk about the application of the law of conservation of mechanical energy.

First of all, the conservation of mechanical energy is for the system, not for individual objects. Such as: earth and objects, objects and springs, etc. For the conservation of mechanical energy of the system, it is necessary to select the reference frame appropriately, because whether the mechanical energy of a mechanical system is conserved is related to the selection of the reference frame.

Conversion into other forms of energy entropy increases.

During movement, energy is dissipated, e.g. into heat.

To put it simply, all energy tends to be more converted in the direction of heat (entropy increase principle).

The object rubs against the air. Generates heat and consumes mechanical energy. or converted into other forms of energy existence.

This is a profound problem, first of all, it is affected by friction, that is, dissipative force, the total mechanical energy of the system must be constantly decreasing, and converted into internal energy, which is the principle of entropy increase, that is, the movement of matter tends to be disordered, and various energies tend to be transformed into internal energy; However, the total momentum is constant, because the universe is an isolated system, and its internal dissipative forces have no effect on the overall momentum, and if the center of mass of the universe is considered to be stationary, then according to the big ** theory, its total momentum is zero (momentum is the superposition of vectors, and the non-absolute values are summed).

As a simple example, in the study of the two-body problem, since there is a certain recovery coefficient e, the total kinetic energy after the collision should be reduced, but the conservation of momentum is still true, because the two centroids are not impulsed by an external force.

Returning to the dissipation problem, since it is said that the combined momentum is always zero, the mechanical energy is constantly lost....Isn't the cosmic heat death just around the corner? In fact, the gravitational force between the stars is equivalent to negative entropy, and the increase in entropy cancels it out, and the heat death of the universe becomes unfounded.

Not necessarily.

For example, in a falling ball, the mechanical energy is conserved, but the momentum is not. The condition for conservation of momentum is that the object is not acted upon by external forces.

Conservation of momentum: not affected by external forces;

Conservation of mechanical energy: forces other than gravity and spring force do not do work;

For example, in a smooth horizontal plane, block A with an initial velocity v is touching a stationary block b, and then sticks together and continues to move, and is not affected by external forces during the interaction, so the momentum is conserved.

Because this is a completely inelastic collision.

Loss of kinetic energy. Mechanical energy is not conserved. You can substitute the data in the past questions.

or the assignment method can calculate that the total mechanical energy after the collision is less than before the collision.

So mechanical energy is not necessarily conserved when momentum is conserved.

The conditions for the two conservations are not the same.

The conservation condition for conservation of mechanical energy is ......Only gravity or the elastic force of the spring do the work, so that there can be conservation of mechanical energy.

The condition for the conservation of momentum is that there is no external force in the system, or the external force is zero or negligible. Only then can momentum be conserved, or in a certain direction, momentum can also be conserved, so there is no necessary connection between them.

If you really want to ask why there is no impact, then it is as ...... as your neighbor's name and your nameThere is only a contact at a certain time, and the other ......There is no necessary connection.

Conservation of momentum requires that the impulse of the external force experienced by the system be zero, or in the event of a collision, the internal force is much greater than the external force at the moment. However, the conservation of mechanical energy requires that the work done by the external forces on the system is zero, and the internal forces are only conservative forces, such as gravity, elastic force, and gravitational force. There are two conservation laws, one of which observes the accumulation of force over time, i.e., impulse.

One observation is the accumulation of force on space, that is, work. Therefore, the conservation conditions of the two are inconsistent.

For example, when two small balls collide completely inelastically, the momentum is conserved because there is only internal force acting, but there is a loss of energy, so the mechanical energy is not conserved.

Conservation of momentum is one of the earliest conservation laws discovered. If a system is not subjected to an external force or the vector sum of the external forces is zero, then the total momentum of the system remains the same, and this conclusion is called the law of conservation of momentum. The law of conservation of momentum is one of the most important and universal conservation laws in nature, which applies to both macroscopic objects and microscopic particles; It is suitable for both low-speed moving objects and high-speed moving objects; It applies to both conservative and non-conservative systems.

Conservation of mechanical energy means that the potential energy (gravitational potential energy or elastic potential energy) and kinetic energy of an object are converted into each other when the work is done by a conservative force such as gravity (or the elastic force of a spring), but the total mechanical energy remains unchanged.

Because there are other forces to work! For example, if you are jumping in a sky, you will have friction, or you will fall to your death! But he also descended at a uniform speed, and the mechanical energy was balanced. It's because of the external workmanship! And friction has an effect on speed! Would?

Conservation of mechanical energy condition:

aObjects are subject to gravity only.

b. The object is not only subjected to gravity but also other forces, but the other forces do not do work, only gravity does work.

c The object is subjected to not only gravity but also other forces, and other forces also do work, but the algebraic sum of the work done by other forces is zero.

If you meet any of the above conditions, you can do it.

Conservation of momentum: the resultant external force is zero, and the momentum of the object is conserved (here only the resultant external force is required to be zero, regardless of the force; If two objects interact with each other, they can be seen as a whole, and the force acting between them is an internal force).

There is conditional conservation, and there is no reason why this is so.