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

As forças conservativas podem ser expressas em termos de energia potencial.
Considere um corpo se movendo ao longo de uma linha reta devido a uma força conservativa que é uma função da posição.
Agora, o trabalho feito pela força conservadora é igual ao negativo da mudança em sua energia potencial.
O trabalho realizado também é igual ao produto da força e ao deslocamento causado pela força.
Assim, a força sobre o corpo é igual ao negativo da mudança na energia potencial dividido pelo deslocamento. 
O sinal negativo indica que a força conservativa arrasta o sistema para uma energia potencial mais baixa.
Para deslocamentos muito pequenos, a expressão de força e energia potencial em uma dimensão pode ser estabelecida.
Para verificação da relação força e energia potencial, considere o exemplo da energia potencial elástica. Quando substituída na relação força e energia, a fórmula para a lei de Hooke é estabelecida.

força e energia potencial em uma dimensão

A força pode ser calculada a partir da expressão para energia potencial, que é uma função da posição. A componente de uma força conservativa, em uma direção particular, é igual ao negativo da derivada da energia potencial correspondente em relação ao deslocamento nessa direção. Para regiões onde a energia potencial muda rapidamente com o deslocamento, o trabalho realizado e a força são máximos. Além disso, quando a força é aplicada ao longo do eixo de coordenadas positivo, a energia potencial diminui com o aumento do deslocamento. Portanto, a força e a derivada da energia potencial em relação ao deslocamento têm sinais opostos.

Por exemplo, se a energia potencial de uma partícula em movimento unidimensional ao longo do eixo x for

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_1.png" style="height: 32px;" />

onde c = 8 N/m3, qual será a força relacionada à energia potencial fornecida? Neste caso, a quantidade conhecida é a energia potencial. A quantidade desconhecida, força, precisa ser calculada.

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_2.png" style="height: 32px;" />

Incorporando o valor da energia potencial na expressão acima, a força ao longo da direção x é calculada como −cx3. Substituindo o valor de c, a força é calculada como −8x3.

A função de energia potencial para a força entre dois átomos em uma molécula diatômica é dada por, aproximadamente

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_3.png" style="height: 32px;" />

onde a e b são constantes e x é a distância entre os átomos. Se a energia de dissociação da molécula for

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_4.png" style="height: 14px;" />

qual é o valor de D? Neste caso, a quantidade conhecida é a energia potencial. A quantidade desconhecida é a energia de dissociação da molécula. Substituindo a função de energia potencial, obtemos a expressão para a força. Como a força líquida é zero no equilíbrio, obtemos

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_5.png" style="height: 32px;" />

Agora, o valor de x6 é substituído na expressão para a energia potencial. Como a energia potencial no infinito é zero, a energia de dissociação da molécula é calculada como b2/4a.

Este texto foi 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>.

Força e Energia Potencial em Uma Dimensão

A força pode ser calculada a partir da expressão da energia potencial, que é uma função da posição. O componente de uma força conservadora, em um particular ...

Education

JoVE Core

Física

Unit 1

Unidade 1

Potential Energy and Energy Conservation

Energia Potencial e Conservação da Energia

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

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work done on a system by external force

External Work, Energy, and Thermal Loss

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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

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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 - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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.

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Types of Kinetic Energy

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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

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Conservation of Mechanical Energy

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Conservative Forces

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PS.Phy.6.1

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Work-Energy Theorem for Motion Along a Curve

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Finding Force from Potential Energy

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