What Is the Formula For Potential Energy?

Potential energy is the energy stored in a system, which can also be released or transformed into other forms of energy. Potential energy is a state quantity, also known as potential energy. Potential energy is not owned by individual objects, but shared by interacting objects.

Potential energy can be divided into gravitational potential energy, elastic potential energy, electric potential energy, and nuclear potential energy according to the nature of the action. The potential energy in mechanics has gravitational potential energy and elastic potential energy. ^[1-2]

Chinese name: Potential energy
Foreign name: potential energy

Definition: The energy of an object due to its position or shape
Category: Gravitational potential energy, elastic potential energy, etc.

Potential energy definition

When the interaction force is "dissipative force" (such as friction), let the object move from point A (assuming it is the potential zero point) to point B to overcome its work as W. When the object returns from point B to point A, It cannot do work on the object (for example, when doing work against friction, the kinetic energy of the object is converted into internal energy, and it is not possible to use this internal energy to do work on the object), so it cannot be said that the object has potential energy due to the existence of the dissipative force. In contrast, if the above process is performed under the action of conservative force, then when the object returns from B to A, the work done by the conservative force on the object is exactly equal to W. This is because the work done by the conservative force is only related to the object. The initial and final relative positions are related. If the object is not subject to other forces, then this work W gives the object the same amount of kinetic energy. So we say that the object has potential energy W at point B. In short, the magnitude of the potential energy is measured by the work done by the conservative forces between the objects in the system. Potential energy is the energy that belongs to the physical system. Generally speaking, the potential energy of an object is actually a brief term. Potential energy is a relative quantity. Choose different potential energy zeros, the values of potential energy are generally different. ^[3]

Potential energy category

Potential energy is divided into gravity potential energy, magnetic field potential energy, elastic potential energy, molecular potential energy, electric potential energy, and gravitational potential energy ^[3] .

Potential energy is infinite energy.

[Gravitational potential energy] (gravitational potential energy) is the energy possessed by the object due to gravity, the formula is EP = mgh (m mass, g should be taken as 9.8N / kg, h the height of the object according to the horizontal plane).

[Magnetic field potential energy] is the magnetic field gravitational or repulsive force that changes the relative position between objects; the energy of a substance that changes its internal characteristics is called magnetic field potential energy. (The magnetic field is a non-conservative field and has a spin field, and the potential energy should exist in a potential field. One of the conditions for a potential field is a spin-free field, so I question the claim of the potential energy of the magnetic field)

[Elastic potential energy] (elastic potential energy) is the energy that an object has due to its elastic deformation. The formula is EP = 1/2 kx ^ 2

[Molecular potential energy] is the energy generated by the interaction force between molecules, which is divided into repulsive force and gravitational force. It is relatively balanced at the equilibrium position, repulsive force when it is smaller than the equilibrium position, and gravitational force when it is larger than the balanced position. At any time, gravity and repulsion coexist.

[Potential energy] The electromagnetic load in the electric field is called potential energy because of its position.

In fact, the potential energy Ep has a certain relationship with the force F and the distance h (the elastic potential energy is x, the gravitational potential energy is r, etc.), which is d (Ep) / dh = F. It can also be written as Ep = Fdh, which is the magnitude of the work done by the conservative force. ^[4]

Potential energy

Due to the mutual forces between molecules, there is energy related to their relative positions, that is, molecular potential energy. Including molecular kinetic energy and molecular potential energy. Every molecule has kinetic energy; there is potential energy between the interacting molecules (but there is no interaction force between ideal gas molecules, so there is no molecular potential energy).

Potential energy relativity

The mass of particle 1 is m, the mass of particle 2 is M, and the two particles are separated by r. They are not subject to any external force. Only the universal gravitation between the two particles is considered.

Assume that at t = 0 the two mass points are relatively stationary, and the gravitational force between the two mass points is F, then the two mass points are moving toward each other from the rest at the same time. The velocity is v, the two particles meet after time t, the displacement of m is s, the displacement of M is S, | s | + | S | = r.

F = GMm / r ^ 2 = ma = MA The gravitational forces on two particles are always equal, but increase with distance.

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

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

Then the displacements of the two particles are also different.

The values of S and s need to be settled using calculus. The process is more complicated, and the process is ignored. The results are as follows:

S = rm / (M + m)

s = rM / (M + m)

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

What kind of point is it?

Assumption: there is a rigid bar connected between two mass points. Use a thin line to tie the midpoint of the mass and drag the thin line upward. The straight bar connecting the two mass points will be perpendicular to the thin line. The midpoint of the mass point is the location of the overall mass point, which is the center of gravity or center of mass of the two mass points.

The potential energy when m is stationary is: EP1 = mah = m (GM / r ^ 2) (rM / (M + m)) = GM ^ 2m / r (M + m)

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

The above analysis is that the two mass points move towards the mass midpoint at the same time, which is a frame of reference established based on the mass midpoint.

What if we set up the frame of reference with m and M, respectively?

To establish a frame of reference with M, then:

The potential energy when m is stationary is: EP = mah = m (GM / r ^ 2) r = GMm / r

The potential energy when M is stationary is: EP = Mah = M (Gm / r ^ 2) r = GMm / r

EP = EP1 + EP2

It can be seen that the potential energy of the particle is related to the reference system, that is, when talking about the potential energy of the particle, it is necessary to talk about the relative potential energy.

Establish a reference frame with M, the potential energy of M is 0, and the potential energy of m is GMm / r; Establish a reference frame with m, the potential energy of m is 0, and the potential energy of M is GMm / r. System, the sum of the potential energy of M and m is GMm / r.

Conclusion: In one-dimensional space, the potential energy of a particle is related to the reference system, but the potential energy formula is equivalent in different reference systems. Similarly, in three-dimensional space, the potential energy of a 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 Potential Science

Potential energy refers to the energy that an object (or system) has due to its position or configuration. For example, the pile hammer lifted to the stern has potential energy, so when it falls 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 it does work on the arrow when the energy is released And shoot it towards the target.

The potential energy of an object (or system) can only be calculated for the selected initial configuration. The amount of potential energy of an object in a particular configuration is equal to the amount of work done by the outside world to overcome the object's resistance when the object is changed from the initial configuration to this configuration without acceleration. . Assuming that the object is subjected to the force F , the element work of the micro-displacement dr is F · dr . If 0 is taken as the zero potential energy position, the potential energy of the object at M point is:

It should also be pointed out that the force acting on the system must be a force that can be restored, such as gravity and elastic force, that is, in a cycle of the system's configuration change, the work of the force is equal to zero, and the formula is as follows:

Forces that meet the above conditions are called conservative forces. In this way, the potential energy of the system depends only on the initial and final position or configuration, and has nothing to do with the path in the process of change. Therefore, the integration route in equation (6) can take any curve from point O to point M. Non-conservative forces (such as friction) do not have potential energy. Here are three potential energies common in general mechanics:

Potential energy gravity potential energy

Gravity is a conservative force. An object with mass m is subject to mg ( g = 9.80665 m / s is the acceleration due to gravity). If the ground is selected as the zero potential energy position, the gravitational potential energy of the object at is:

More strictly, this is the potential energy of a system of objects and the earth (Figure 1)

Potential energy

When the distance r between the object and the center of the earth is large, the change of gravity with distance must be considered (Figure 2). The gravity of an object of mass m is

Where

Is the mass of the earth; G = 6.673 × 10 m / (kg · s), which is the gravitational constant. The potential energy can be calculated from equation (6) as:

Where

= 6.371 × 10 meters, which is the radius of the earth. The position of zero potential energy is still taken on the surface of the earth.

The gravitational potential energy between any two objects also has gravitational potential energy. For example, the gravitational potential energy of two stars that can be regarded as particles with mass m ₁ and m ₂ is

Where r is the distance between the two stars.

Potential energy

When the spring deforms, the amount of elastic force F acting on the outside and the deformation

Directly proportional

(Hooke's law), k is the spring stiffness (Figure 3). Elastic force is also conservative. 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 is calculated from equation (6) as:

Potential energy

Definition: The charge in the electric field is called potential energy because of its position.

Can also be defined like this:

(1) The energy that a charge has in an electric field.

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

Formula: Ep = WAO = q · A. (Ep represents potential energy):

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

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

Potential energy in an electrostatic field. The difference between the potential energy of a point of charge at two points in an electrostatic field is equal to the work done by the electrostatic force when it moves from one point to another.

Potential energy reflects the energy that an electric field and a charge in it have in common.

The potential energy can be obtained by the work of the electric field force, because W AB = qUAB = q (A- B) = qA-qB = EA (beginning) Eb (last) =- E,

(EA (beginning) and EB (end) are the potential energy of two points).

The relationship between electric field force work and electric potential energy change:

WAB> 0, Ep <0, the electric field force does positive work, and the potential energy decreases to transform into other forms of energy;

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

Moving along the electric field line, A B moves, if it is a positive charge, then WAB> 0, then UAB = A-B> 0, then , then positive Ep

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

Against the electric field line, B A moves. If it is a positive charge, then WAB <0, then UAB = A-B <0, then , then positive Ep ;

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

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

Wab = Epa-Epb

The potential energy formula is related to the electric field, the electric charge in the electric field, and the selection of the zero point of the potential energy. For an electrostatic field generated by a point charge (electric quantity q), the potential energy is the distance r from the space position where the charge q is located to the point charge location It has the following relationship: We = kQq / r. Where k is a constant.

Note here that there is no negative sign, which is different from the gravitational potential, because the direction of gravitation is directed to the other side. When Q and q are positive signs, the electric field force (Coulomb force) is mutually exclusive.

The method of judging the potential energy: 1 field source charge judgment method-the closer to the positive charge of the field source, the larger the potential energy of the positive charge, and the smaller the potential energy of the negative charge.

2 Electric field line method-When a positive charge moves in the direction of the electric field line, the potential energy gradually decreases, and when it moves against the direction of the electric field line, the potential energy gradually increases.

3 Work judgment method-Regardless of the positive and negative charges, the electric field force does positive work, the potential energy of the charge must decrease, and the electric field force does negative work, the potential energy of the charge must increase.

The zero potential energy can be arbitrarily selected, but in theoretical research, the potential energy at infinity is often taken to be zero.

Take infinity as potential zero: in the electric field generated by positive charge > 0, away from the field source charge : move the positive test charge W> 0, Ep

Move negative test charge W <0, Ep .

In the electric field generated by negative charge <0, away from the field source charge : moving positive test charge W <0, Ep

Move the negative test charge W> 0, Ep .

Attached:

1. Only under the effect of electric field forces:

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

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

2. Not only affected by electric field forces:

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

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

Potential energy conclusion

By definition, as long as an object can do work, it can be said that it has potential energy. When the mass is the same, the greater the speed of motion, the greater its kinetic energy; the greater the mass of an object with the same speed, the greater its kinetic energy.

Potential Energy Marketing

Potential marketing means that in the long-term marketing practice, companies are pursuing a sales state. For example, through marketing operations, products are introduced from the introduction period and quickly enter the growth period, and gradually form a stable sales growth trend. This may be the situation that all businesses would like to see. But in fact, many companies' products are often just put on the market and soon disappear. The main reason for the failure of this product is that it did not build well in the early stages of market operation. To this end, the concept of potential energy marketing was proposed to help the company's products smoothly enter the growth phase from the introduction period, and put the entire marketing work The state of a virtuous circle.

Potential energy in physics can basically be defined as the energy determined by the relative positions of parts of an object. We all know that any product is valuable. When this product is accepted by the market, there will be a kind of transfer value in the transaction. The greater the value of this transfer, the more attractive it is to the customer. From customer value to product value, a level difference is formed. This level difference can be called "potential". Establishing a trend is the process of carrying out value-added activities from product value to customer value, so that customers form and maintain a highly attractive process for the product. Therefore, potential energy marketing can be defined as: a company's marketing activities in order to make products flow to customers in the process of forming value-added differences.

This value added difference can be divided into positive difference and negative difference. A positive difference means that the customer's transfer value is positive, and a negative difference means that there is no customer transfer value, or the customer's transfer value is zero or negative. Since the US marketing scholar Michael Porter put forward the value chain theory, many Chinese companies have tried value-added services and pursued maximum customer value, but many companies just stayed on the idea and did not really put it into action. Potential energy marketing starts from researching the psychology of customers, and emphasizes that the customers add value in the process from cognizing and receiving products to evaluating products, so as to make product sales form a stable growth trend.

Potential energy exchange

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

It can be seen in the roll experiment that the roll spins down and turns faster and faster. At the lowest point, the roll turns and rises, and it turns slower and slower until it returns to its original position. Then it falls and rises again, repeating the original movement. As the roll descends, its gravitational potential energy becomes smaller and smaller, and its kinetic energy becomes larger and larger, and the gravitational potential energy is converted into kinetic energy. As the roll rises, its kinetic energy becomes smaller and smaller, and the gravitational potential energy becomes larger and larger, and 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, let the wooden ball roll from the chute into the horizontal groove. A spring leaf is erected in the horizontal groove, and its lower end is fixed. Observe the process of collision between the wooden ball and the spring leaf. After the wooden ball contacts the spring piece, the spring piece is bent (A B), the kinetic energy of the wooden ball decreases, and the elastic potential energy of the spring piece increases. In the process, the kinetic energy is converted into elastic potential energy. Immediately afterwards, the spring piece returned to its original shape and bounced the wooden ball back (B C). In the process, the elastic potential energy was converted into kinetic energy. ^[2]

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

In the figure, if the entire process of sliding the wooden ball from the chute to the maximum extent of the spring sheet being pressed and bent is considered, the potential energy of gravity is converted into the kinetic energy of the wooden ball, and finally the elastic potential energy of the spring sheet. When the spring sheet returns to its original shape, the wooden ball can move to a certain height on the chute, that is, the elastic potential energy is converted into the gravity potential energy. ^[2]

Potential Energy Related Exercises

For example, stones thrown vertically, excluding air resistance, during the ascent process ()

A. Reduced kinetic energy, unchanged gravitational potential energy

B. The kinetic energy does not change and the gravitational potential energy increases

C. Kinetic energy decreases and gravitational potential energy increases

D. Constant kinetic energy and constant gravitational potential energy

analysis:

Judging the change of kinetic energy mainly depends on the change of the object's moving speed, and the increase of the speed increases the kinetic energy of the object; judging the change of the potential energy of gravity mainly depends on the change of the height of the object, which increases as the height of the object increases. It mainly depends on the degree of elastic deformation. The following table:

can	With what	Determine if you have	Judge change
kinetic energy	m, v	motion	speed
Gravitational potential energy	m, h	Relative height	height
Elastic potential energy	Degree of deformation	Elastic deformation	Degree of deformation

The stones that are thrown up continuously rise, the height increases, so the potential energy of gravity increases; in the process of ascending, the speed decreases continuously, so the kinetic energy decreases continuously.

Answer: C

note:

To judge the change of kinetic energy and gravity potential energy, it is mainly to see the changes in the speed and relative height of the object, because the mass of the object is unchanged (specific analysis of specific problems).