Name: finding force from potential energy
Uploaded: 2023-04-30T10:57:22.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physics

Energy

PS.Phy.6.2

force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

Las fuerzas conservadoras pueden expresarse en términos de energía potencial.
Considere un cuerpo que se mueve a lo largo de una línea recta debido a una fuerza conservadora que es una función de la posición.
Ahora bien, el trabajo realizado por la fuerza conservadora es igual al negativo del cambio en su energía potencial.
El trabajo realizado también es igual al producto de la fuerza y al desplazamiento causado por la fuerza.
Por lo tanto, la fuerza sobre el cuerpo es igual al negativo del cambio en la energía potencial dividido por el desplazamiento. 
El signo negativo indica que la fuerza conservadora arrastra el sistema a una energía potencial más baja.
Para desplazamientos muy pequeños, se puede establecer la expresión de la fuerza y la energía potencial en una dimensión.
Para verificar la relación entre la fuerza y la energía potencial, considere el ejemplo de la energía potencial elástica. Cuando se sustituye en la relación de fuerza y energía, se establece la fórmula de la ley de Hooke.

fuerza y energía potencial en una dimensión

La fuerza se puede calcular a partir de la expresión para la energía potencial, que es una función de la posición. El componente de una fuerza conservativa, en una dirección particular, es igual al negativo de la derivada de la energía potencial correspondiente con respecto al desplazamiento en esa dirección. Para las regiones donde la energía potencial cambia rápidamente con el desplazamiento, el trabajo realizado y la fuerza son máximos. Además, cuando se aplica fuerza a lo largo del eje de coordenadas positivo, la energía potencial disminuye con un aumento en el desplazamiento. Por lo tanto, la fuerza y la derivada de la energía potencial con respecto al desplazamiento tienen signos opuestos. 

 Por ejemplo, si la energía potencial de una partícula en movimiento unidimensional a lo largo del eje x es
 <img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_1.png" style="height: 32px;"> 

 donde c = 8 N/m3, ¿cuál será la fuerza para la energía potencial dada? Aquí, la magnitud conocida es la energía potencial. La magnitud desconocida, la fuerza, debe ser calculada. 
 <img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_2.png" style="height: 32px;"> 

 Incorporando el valor de la energía potencial en la expresión anterior, se calcula que la fuerza a lo largo de la dirección x es -cx3. Sustituyendo el valor de c, se calcula que la fuerza es -8x3. 

 La función de energía potencial para la fuerza entre dos átomos en una molécula diatómica se da aproximadamente por, 
 <img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_3.png" style="height: 32px;"> 

 donde a y b son constantes y x es la distancia entre los átomos. Si la energía de disociación de la molécula es,
 <img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_4.png" style="height: 14px;"> 

 ¿cuál es el valor de D? Aquí, la magnitud conocida es la energía potencial. La magnitud desconocida es la energía de disociación de la molécula. Sustituyendo la función de energía potencial, obtenemos la expresión para la fuerza. Dado que la fuerza neta es cero en el equilibrio, obtenemos 
 <img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_5.png" style="height: 32px;"> 

 Ahora, se sustituye el valor de x6 en la expresión para la energía potencial. Dado que la energía potencial en el infinito es cero, se calcula que la energía de disociación de la molécula es b2/4a. 

 Este texto está adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/8-4-potential-energy-diagrams-and-stability">Openstax, University Physics Volume 1, Section 8.4: Potential Energy Diagrams and Stability</a>.

Fuerza y Energía Potencial en una Dimensión

La fuerza se puede calcular a partir de la expresión de la energía potencial, que es una función de la posición. El componente de una fuerza conservadora, en un ...

Education

Educación

JoVE Core

Física

Unit 1

Unidad 1

Potential Energy and Energy Conservation

Energía Potencial y Conservación de la Energía

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

finding force from potential energy

Force can be found from potential energy when the energy is written as a function of position. For a conservative force, the force component in a given direction equals the negative derivative of the matching potential energy with respect to displacement. This means force and the slope of potential energy have opposite signs.

Where potential energy changes quickly with displacement, the force and the work done are largest. When a force acts along the positive coordinate axis, potential energy decreases as displacement increases. In one-dimensional motion, this relationship is often used to move from a known potential energy function to the force it produces.

For example, if a particle moves along the x-axis and its potential energy is given with c = 8 N/m^3, the force can be calculated from that expression. The potential energy is the known quantity, and the force is the unknown quantity. Differentiating the energy function gives the x-direction force as -cx^3, which becomes -8x^3 after substituting the value of c.

The same idea also applies to the force between two atoms in a diatomic molecule. Their potential energy can be written approximately as a function of distance x, with a and b as constants. If the dissociation energy is needed, the force is first found from the potential energy, and the equilibrium point is used because the net force is zero there. Then the value of x^6 is substituted into the energy expression, and since the potential energy at infinity is zero, the dissociation energy is b^2/4a.

Finding Force from Potential Energy

gravitational potential energy

Gravitational Energy from Height and Weight

Gravitational potential energy depends on an object’s weight and its height above the ground. It is one part of the total potential energy of a system, which comes from the interactions between objects. In a system, the total potential energy is the sum of the potential energies for all the objects. Potential energy is usually grouped into two main categories: gravitational potential energy and elastic potential energy. Gravitational potential energy describes the energy tied to a body’s...

elastic potential energy

Spring Force and Stored Energy

Elastic potential energy is stored when an elastic object is deformed, such as when a spring is stretched. An object is elastic if it returns to its original shape and size after the force is removed. This stored energy is part of a system’s potential energy. An ideal spring also exerts an elastic force. The work done by this force can be described as a change in the spring’s elastic potential energy. For a perfectly elastic spring in one dimension, that work depends only on the spring...

conservation of mechanical energy

Mechanical Energy in Isolated Systems

Mechanical energy in an isolated system is the total of kinetic energy and potential energy. Kinetic energy is the energy of motion, and potential energy is stored energy. The transcript focuses on what happens when energy shifts within a system without outside influence. In this case, only conservative forces act on the objects in the system. Conservative forces can transfer energy between kinetic energy and potential energy. Friction and drag do not act here, and no external force from...

/files/media/science-education/science-education-thumbs/14702.jpg

work done on a system by external force

External Work, Energy, and Thermal Loss

External work on a system can change its energy in more than one way. For a single particle, work done by an external force changes kinetic energy. For a system of interacting particles, internal forces also matter, and potential energy helps describe their effect. The net work done by an external force can be written as the total change in mechanical energy. Mechanical energy includes both kinetic energy and potential energy. When the system gains or loses this energy, the work expression...

/files/media/science-education/science-education-thumbs/14751.jpg

conservative forces

Conservative Forces and Path Independence

Conservative forces are forces for which the work done depends only on the starting and ending points. In this case, the work is path independent. That means the total energy of the system, including kinetic energy and potential energy, stays conserved during the change. This idea follows the law of conservation of energy. When energy shifts between kinetic and potential forms, the total amount remains the same. Because the work is completely reversible, an object can start and stop at any two...

non-conservative forces

Friction and Energy Loss in Motion

Non-conservative forces, such as friction and air resistance, remove energy from a system as it moves. The energy is not stored as potential energy. Instead, it is lost from the system and cannot be used later for useful work. These forces are path-dependent, which means the route matters. Where an object starts and stops can change the work done. A grinding wheel is one example, because the work depends on how many rotations the wheel makes. Non-conservative forces also turn large-scale...

conservation of energy

Energy Changes in a Closed System

Energy changes in a closed system follow a conservation law in physics. A conserved quantity is not the same as the everyday use of the word "conserved." In science, a conserved quantity stays constant, or it changes by a definite amount that is transferred to another system and converted into another form of the same quantity. This means a conserved quantity can change form, but it cannot be created or destroyed in a strict physical sense. For that reason, physics does not have a law of...

conservation of energy: application

Energy Conservation Problem-Solving Steps

Energy conservation problem-solving uses a clear set of steps. First, identify the system you want to study. In many cases, that system includes more than one body at the same time. Next, identify the forces acting on the object and decide whether each force is conservative. A conservative force is one whose work can be described with potential energy. If a non-conservative force such as friction does work, then mechanical energy is not conserved, and the system must be analyzed with...

force and potential energy in one dimension

Force can be found from potential energy when the energy is written as a function of position. For a conservative force, the force component in a given direction equals the negative derivative of the matching potential energy with respect to displacement. This means force and the slope of potential energy have opposite signs. Where potential energy changes quickly with displacement, the force and the work done are largest. When a force acts along the positive coordinate axis, potential energy...

force and potential energy in three dimensions

force-and-potential-energy-in-three-dimensions

Gradient Force from 3D Potential Energy

Gradient force from 3D potential energy shows how a conservative force changes along the x, y, and z axes. The potential energy function U depends on all three spatial coordinates. Each force component is linked to how U changes with position along one coordinate. In one dimension, force can be written as the negative ratio of the change in potential energy to the displacement along that axis. For very small displacements, these ratios become derivatives. When a function has several variables,...

energy diagrams - i

Potential Energy Diagrams and Stability

Potential energy diagrams help describe how a mechanical system moves. Because energy is a scalar quantity, the system’s behavior is easier to interpret from the diagram. A skater on a parabolic ramp is a clear example. The ramp height changes with horizontal position, so the potential energy changes as well. As the skater moves down from the highest point, potential energy changes into kinetic energy. Kinetic energy is the energy of motion. The net force on the skater is gravitational force,...

energy diagrams - ii

Stability in Potential Energy Diagrams

Potential energy diagrams show how stable a system is at different positions. Their shape, or topology, helps identify equilibrium points. An equilibrium point is a place where the system can stay in balance because the net force is zero. At a local minimum, the potential energy is lowest. The system tends to remain there unless a net force acts on it. The slope at the minimum is zero. The slope is positive on both sides, so the force acts as a restoring force and pushes the system back. A...

key terms and concepts

Learn how to calculate force from potential energy in one dimension, including the sign rule, a particle example, and dissociation energy for atoms.

Finding Force from Potential Energy | JoVE K12

physics

JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

Pennsylvania State Academic Standards

Physical Science

3.2.9-12.S

Louisiana Student Standards for Science

High School

HS-PS3-5

Tennessee Academic Standards

PHYS.PS3.3

PHYS.PS3.8

Virginia  Standards of Learning

HIgh School

PH.4

PH.4.b

Alabama Course of Study Science

9-12.P.2.3.b

Next Generation Science Standards

HS-PS3-2

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS3-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-2.

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

Types of Potential Energy

Potential energy is also known as energy at rest or stored energy. Common types of potential energy include the gravitational potential energy stored in ...

Types of Kinetic Energy

The amount of kinetic energy of an object depends on its mass and speed. Consider two balls of different masses rolling down an inclined plane at the same ...

Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Elastic Potential Energy

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is ...

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

Conservative Forces

According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the ...

Non-conservative Forces

Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike ...

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Use models to qualitatively and quantitatively analyze the kinetic and potential energy in a system.

PS.Phy.6.1

Work

Work is done when energy is transferred from one object to another. In other words, work is when a force acts on something that undergoes a displacement ...

Positive, Negative, and Zero Work

Work is done on an object when energy is transferred to the object. In other words, work is done when a force acts on a body that undergoes a displacement ...

Work-energy Theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared ...

/files/media/science-education/science-education-thumbs/14699.jpg

work-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

/files/media/science-education/science-education-thumbs/14700.jpg

Work Done Over an Inclined Plane

The center-of-mass framework helps to easily describe the work done on rigid bodies. Since the internal forces in a rigid body do no work, they can be ...

/files/media/science-education/science-education-thumbs/14701.jpg

Work Done by Many Forces

The total work done on an object acted upon by multiple forces can be computed using two methods that give the same result. In one method, the work done ...

/files/media/science-education/science-education-thumbs/14735.jpg

Work Done by Gravity

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
Like other forces, ...

/files/media/science-education/science-education-thumbs/14750.jpg

Power

The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its ...

Power Expended by a Constant Force

The relationship between work done and the time taken to do it can be explained using the concept of power. For example, several sprinters in a race may ...

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular ...

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function ...

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the ...

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Analyze and interpret data to qualitatively and quantitatively explain the relationship among work, power, and energy.

Understand the relationship among work, energy, and power.

Finding Force from Potential Energy

Description

Transcript

Tags

More videos by Standards