potential energy

[shì néng]

Energy stored in the system

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zero Useful+1

zero

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

Potential energy is the energy stored in a system, which can also be released or transformed into other forms of energy. The potential energy is State quantity , also known as potential energy 。 The potential energy does not belong to the individual objects, but to the interacting objects.

Potential energy can be divided into Gravitational potential energy , elastic potential energy, electric potential energy, nuclear potential energy, etc. Potential energy in mechanics includes gravitational potential energy and elastic potential energy.^[1-2]

Chinese name: potential energy
Foreign name: potential energy

Interpretation: Energy possessed by an object due to its position or configuration
Category: Gravitational potential energy , elastic potential energy, etc

catalog

definition

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When the interaction force is“ Dissipative force ”(e.g friction ）When, set object Move from point A (assuming it is the zero point of potential energy) to point B to overcome it Work It is W, when the object returns from point B to point A, it cannot do work on the object (for example, when overcoming friction, the kinetic energy of the object is converted into internal energy, and this part of internal energy cannot be used to do work on the object), so it cannot be said that the object has potential energy due to the existence of dissipative force. On the contrary, if the above process is Conservatism When the object returns from B to A, Conservatism The work done on the object is exactly equal to W, because Conservatism The work done is only relative to the initial and final of the object position of If the object is not affected by other forces, this work W will make the object get the same amount of kinetic energy 。 So we say that the object has potential energy W at point B. In a word, the magnitude of potential energy is measured by the work done by the conservative force between objects in the system. The potential energy is common to the body system energy It is generally said that the potential energy of an object is actually a brief statement. The potential energy is a Relative quantity 。 When different potential energy zeros are selected, the values of potential energy are generally different.^[3]

Molecular potential energy

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Due to the existence of mutual Force Therefore, it has the energy related to its relative position, that is, molecular potential energy. include Molecular kinetic energy And molecular potential energy. Every molecule has kinetic energy; There is potential energy between interacting molecules (but ideal gas No intermolecular Interaction force , there is no molecular potential energy).

Relativity

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potential energy

particle The mass of 1 is m, the mass of particle 2 is M, the distance between the two particles is r, without any external force, and only the Universal gravitation ，

Assume: when t=0, two particles Relative static , the universal gravitation between the two particles is F, then the two particles move from static to the other at the same time, the acceleration of M is A, the acceleration of m is a, the speed of M is V, the speed of m is v, the two particles meet after time t displacement Is s, and the displacement of M is S, | s |+| S |=r.

F=GMm/r ^ 2=ma=MA The universal gravitation of two particles is always equal, but increases with the shortening of distance.

A=Gm/r ^ 2; a=GM/r ^ 2 The accelerations of the two particles are different, and both increase with the shortening of the distance.

V=At=Gmt/r ^ 2; v=at=GMt/r ^ 2 The velocities of the two particles are also different, and both increase with the shortening of the distance.

Then the displacement of the two particles is also different.

The values of S and s need to be settled by calculus. The process is complex. The process is ignored. The results are as follows:

S=rm/(M+m)

s=rM/(M+m)

The point where two particles meet is called the midpoint, and the r/2 point is called the midpoint. The midpoint is between the large particle and the midpoint.

What kind of point is the midpoint of quality?

Assume that there is a rigid straight bar between the two particles, tie the thin line to the middle of the particle, pull the thin line upward, and the straight bar connecting the two particles will be perpendicular to the thin line. If the two particles are regarded as a whole, then the middle of the two particles is the location of the whole particle, that is, the whole of the two particles focus Or centroid.

The potential energy of m at rest is: EP1=mah=m (GM/r ^ 2) (rM/(M+m))=GM ^ 2m/r (M+m)

M The potential energy at rest is: EP2=Mah=M (Gm/r ^ 2) (rm/(M+m))=GMm ^ 2/r (M+m)

The above analysis considers that the two particles move towards the middle of the mass at the same time, which is based on the middle of the mass Reference system 。

What if we set up the reference system with m and M respectively?

If the reference system is established with M, then:

M The potential energy at rest is: EP=mah=m (GM/r ^ 2) r=GMm/r

M potential energy at rest: EP=Mah=M (Gm/r ^ 2) r=GMm/r

EP=EP1+EP2

It can be seen that the potential energy of a particle is related to the reference system, that is, when we talk about the potential energy of a particle, we must talk about its relative potential energy.

The reference system is established with M, the potential energy of M is 0, and the potential energy of m is GMm/r; Establish a reference system with m, the potential energy of m is 0, the potential energy of M is GMm/r, and establish a reference system with a point on the line between M and m, the potential energy sum of M and m is GMm/r.

Conclusion: In One-dimensional space The potential energy of the particle is related to the reference system, but the potential energy formula is equivalent in different reference systems. Similarly, in three-dimensional space In, the potential energy of the particle is related to the reference system, but the potential energy formula is equivalent in different reference systems (the argument is omitted).

Potential energy in mechanics

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Potential energy refers to the energy possessed by an object (or system) due to its position or configuration. For example, the heavy hammer of the pile driver lifted to a high place has potential energy, so when falling, it can increase its kinetic energy and do work to the outside world, driving the pile into the soil; The open bow has potential energy, so when releasing energy, do work on the arrow and shoot it at the target.

The potential energy of an object (or system) can only be calculated for the selected initial configuration. The potential energy of an object in a particular configuration is quantitatively equal to the work done by the outside to overcome the resistance of the object when the object is changed from its initial configuration to this configuration without acceleration, that is, the work done by the object resistance in this process is taken as a negative value. Assume that the object is under force F And micro displacement dr The elementary work of is F·dr 。 If point 0 is taken as the position of zero potential energy, the potential energy of the object at point M is:

formula

It is also pointed out that the force acting on the system must be recoverable like gravity and elastic force, that is, in a cycle of system configuration change, the work of the force is equal to zero, and the formula is as follows:

formula

The force meeting the above conditions is called conservative force. In this way, the potential energy of the system only depends on the initial and final positions or configurations, and has nothing to do with the path in the change process. Therefore, the integration path in equation (6) can be taken from O Point to M Any curve of a point. Non conservative forces (such as friction) do not have potential energy. The following three potential energies are common in general mechanics:

Gravitational potential energy

Gravity is a conservative force. Quality is m The gravity of the object is mg （ g =9.80665 m/s two Is the acceleration of gravity). If the ground is selected as the zero potential energy position, the gravity potential energy of the object at height is:

Change of potential energy distribution

More strictly, this is the potential energy of the system composed of objects and the earth (Fig. 1)

Gravitational potential energy

When the distance r of the object from the center of the earth is large, the variation of the gravity with the distance must be taken into account (Figure 2). Quality is m The gravity of the object is

formula

Where

formula

Is the mass of the earth; G =6.673 × 10m/(kg · s) is the gravitational constant. According to equation (6), the potential energy is:

formula

Where

=6.371 × 10m is the radius of the earth. The zero potential energy position is still taken on the earth's surface.

change

The universal gravitation between any two objects also has gravitational potential energy, for example, the mass is m one and m two The gravitational potential energy of two stars that can be regarded as particles of

formula

among r Is the distance between two stars.

Elastic force potential energy

When the spring is deformed, the elastic force F acting on the outside and the deformation

Is proportional,

formula

(Hooke's Law), k Is the spring stiffness (Figure 3). The elastic force is also a conservative force. If the natural state of the spring when it is not deformed is taken as the zero potential energy configuration, the potential energy when it is deformed can be calculated from equation (6) as follows:

formula

Electric potential energy

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definition: charge In the electric field, due to the action of the electric field, the energy determined by the position is called electric potential energy.

It can also be defined as follows:

(1) The energy of an electric charge in an electric field.

(2) The charge q moves from a point A in the electric field to Reference point O， Electric field force The work done is equal to the electric potential energy q has at point A.

Formula: Ep=WAO=q · φ A (Ep stands for electric potential energy):

When φ A>0, q>0, then Ep>0, q<0, then Ep<0;

When φ A<0, q>0, then Ep<0, q<0, then Ep>0

electrostatic field Potential energy in. one Point charge When the difference of electric potential energy between two points in the electrostatic field is equal to that when it moves from one point to another, Electrostatic force Work done.

The electric potential energy reflects the energy shared by the electric field and the charge in it.

The electric potential energy can be obtained from the work done by the electric field force, because W AB=qUAB=q (Φ A - Φ B)=q Φ A-q Φ B=EA (initial) - Eb (final)=- △ E,

(EA (initial) and EB (final) are electric potential energy of two points).

Relation between work done by electric field force and electric potential energy change:

WAB>0， △ Ep<0, electric field force Positive work , electric potential energy is reduced and converted into other forms of energy;

WAB<0， △ Ep>0, electric field force Negative work , electric potential energy increases~other forms of energy are converted into electric potential energy.

along Electric field line , A → B movement, if it is positive charge , then WAB>0, then UAB=Φ A - Φ B>0, then Φ ↓, then positive Ep ↓

if it is negative charge , then WAB<0, then UAB=Φ A - Φ B>0, then Φ ↓, then negative Ep ↑.

Move against the electric field line, B → A, if it is positive charge, WAB<0, UAB=Φ A - Φ B<0, Φ ↑, positive Ep ↑;

If it is negative charge, then WAB>0, then UAB=Φ A - Φ B<0, then Φ ↑, then negative Ep ↓

The work done by electrostatic force is equal to the reduction of electric potential energy

Wab=Epa-Epb

The electric potential energy formula is related to the electric field, the charge in the electric field and the selection of the zero point of the electric potential energy Point charge （ Electricity Is the electrostatic field generated by q), where the electric potential energy and charge q are located spatial location The distance r to the point charge location has the following relationship: We=kQq/r. Where k is constant 。

Notice that there is no minus sign, and Gravitational potential This is because the direction of gravity is pointing at each other. When Q and q are both positive signs, the electric field force（ Coulomb force ）They are mutually exclusive.

Judgment method of electric potential energy: 1 Field source charge Judgment method - departure source positive charge The closer it is, the greater the electric potential energy of positive charge is, and the smaller the electric potential energy of negative charge is.

2 Electric field line method—— positive charge When moving along the direction of the electric field line, the electric potential energy gradually decreases, and when moving against the direction of the electric field line, the electric potential energy gradually increases.

3. Judgment method of work - regardless of positive and negative charges, electric field force Positive work , the electric potential energy of the charge must be reduced, and the electric field force Negative work The electric potential energy of the charge will increase.

The zero potential energy can be chosen arbitrarily, but in theoretical research, the electric potential energy at infinity is often taken as 0.

Take infinity as potential zero: ① Φ>0 in the electric field generated by positive charge, away from Field source charge Φ ↓: moving positive inspection charge W>0, Ep ↓

Moving negative test charge W<0, Ep ↑.

② Φ<0 in the electric field generated by negative charge, keep away from Field source charge Φ ↑: moving positive test charge W<0, Ep ↑

Moving negative inspection charge W>0, Ep ↓.

Attachment:

1. Only under the action of electric field force:

(1) When the electric field force does positive work, the electric potential energy decreases and the kinetic energy increases. That is: electric energy Convert to other forms of energy (kinetic energy).

(2) When the electric field force does negative work, the electric potential energy increases and the kinetic energy decreases. That is, other forms of energy (kinetic energy) are converted into electric energy.

2. Not only under the action of electric field force:

(1) When the electric field force does positive work, the electric potential energy decreases, and how the kinetic energy changes is uncertain.

(2) When the electric field force does negative work, the electric potential energy increases, and how the kinetic energy changes is uncertain.

conclusion

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By definition, as long as a body can do work, it can be said to have potential energy. When the quality is the same, Movement speed The bigger it is, the greater its kinetic energy; The greater the mass of an object with the same speed, the greater its kinetic energy.

Potential energy marketing

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Potential marketing means that enterprises are pursuing a sales state in their long-term marketing practice, such as Through marketing operation, the product will quickly enter the growth period from the introduction period, and gradually form a stable sales growth trend 。 This may be a situation that all enterprises are willing to see. But in fact, the products of many enterprises are often just launched on the market, and soon lost sight. The main reason for the failure of this product is that it did not "build momentum" well in the initial stage of market operation. Therefore, the concept of potential energy marketing was proposed to help enterprises' products enter the growth period smoothly from the introduction period, and make the whole marketing work in a virtuous circle.

physics The potential energy in can basically be defined as the relativity between parts of an object position Determined energy. We all know that any product is valuable. When this product is accepted by the market, it will generate a kind of transfer value in the transaction. The greater the transfer value, the customer The more attractive it is. From customer value to product value, there is a height difference, which we can call "potential". Building momentum is the process of carrying out value-added activities from product value to customer value, so that customers can form and maintain high attractiveness to products. Therefore, potential energy marketing can be defined as: enterprises carry out potential energy marketing in order to create value-added difference (potential) in the process of product flow to customers Marketing Activities.

This value-added difference can be divided into positive difference and negative difference. The positive difference means that the customer's delivered value is positive, and the negative difference means that it does not exist customer delivered value , or the customer's delivered value is zero or negative. since U.S.A Marketing scholar Michael baud Since the value chain theory was put forward, many enterprise They are all trying to provide value-added services and maximize customer value, but many enterprises just stay on the idea and do not really pay for it in action. Potential marketing starts with the study of customers' psychology, emphasizing the value added in the process of customers' cognition of products, acceptance of products, and evaluation of products, so as to form a stable growth trend of product sales.

Momentum exchange

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(1) Kinetic energy and gravitational potential energy can be transformed into each other.

In the rolling pendulum experiment, we can see that the rolling pendulum rotates and drops, and the faster it rotates, the faster it turns. At the lowest point, the roll pendulum turns to rise, and it turns more and more slowly until it almost returns to its original position. Then it goes down and up again, repeating the original movement. When the roll pendulum descends, its gravitational potential energy becomes smaller and smaller, and its kinetic energy becomes larger and larger. The gravitational potential energy is converted into kinetic energy. When the rolling pendulum rises, its kinetic energy becomes smaller and smaller, and its gravitational potential energy becomes larger and larger. The kinetic energy is converted into gravitational potential energy.^[1]

(2) Kinetic energy and elastic potential energy can be transformed into each other

As shown in the figure, roll the wooden ball from the chute into the horizontal groove. A spring plate is erected in the horizontal groove, and its lower end is fixed. Observe the collision process between the wooden ball and the spring piece. After the wooden ball contacts the spring sheet, it bends the spring sheet (A → B). The kinetic energy of the wooden ball decreases, and the elastic potential energy of the spring sheet increases. In this process, the kinetic energy is converted into elastic potential energy. Then, the spring piece returns to its original state and bounces the wooden ball back (B → C). In this process, the elastic potential energy is converted into kinetic energy.^[2]

Illustration

(3) Gravity potential energy and elastic potential energy can be transformed each other

In the figure, if the whole process of the wooden ball sliding from the chute to the maximum bending of the spring plate is considered, the gravitational potential energy is converted into the kinetic energy of the wooden ball, and finally into the elastic potential energy of the spring plate. When the spring piece returns to its original state, the wooden ball can move to a certain height on the chute, that is, the elastic potential energy is converted into the gravitational potential energy.^[2]

Related exercises

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For example, stones thrown vertically, regardless of air resistance

A. The kinetic energy decreases and the gravitational potential energy remains unchanged

B. The kinetic energy remains the same, and the gravitational potential energy increases

C. The kinetic energy decreases and the gravitational potential energy increases

D. Constant kinetic energy, constant gravitational potential energy

analysis:

Judging the change of kinetic energy mainly depends on the change of the moving speed of the object, and the kinetic energy of the object increases when the speed increases; Judging the change of gravity potential energy mainly depends on the change of object height. The gravity potential energy of the object increases with the increase of height; Similarly, the elastic potential energy mainly depends on the degree of elastic deformation. The following table:

can	What is related	Judge whether there is	Judgment change
kinetic energy	m，v	motion	speed
Gravitational potential energy	m，h	Relative height	height
Elastic potential energy	Deformation degree	Elastic deformation occurs	Deformation degree

The upward thrown stones keep rising and the height increases, so the gravitational potential energy increases; In the process of rising, the speed decreases, so the kinetic energy decreases.

Answer: C

be careful:

To judge the change of kinetic energy and gravitational potential energy, we mainly look at the change of the object's motion speed and relative height, because the object's mass remains unchanged (specific analysis of specific problems).

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