Name: stability in potential energy diagrams
Uploaded: 2023-04-30T10:57:45.000Z
Duration: 1 min 10 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

Energy Diagrams - II

Consider a skater skating on a frictionless parabolic ramp, the force acting on the skater is given by the negative slope of the potential energy curve. At the bottom of the ramp, the force acting on the skater is zero.
Consider an imaginary potential energy diagram; the net force acting on the skater will be zero at point x1 and similarly at point x2.
Any displacement away from point x1 will result in a restoring force on the skater,&#160; directed towards the point x1.
Whereas, any displacement of the skater at point x2 will result in a force, directed away from the point x2.
Any minimum point in the potential energy curve is a stable equilibrium point, whereas any maximum is an unstable equilibrium point.
If the total energy of the skater is E2, then the skater will be able to escape and go beyond point x2. But if the total energy is E1, then the skater will be trapped between positions x0 and x2.

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 system.
The point in the energy diagram at which the system&#8217;s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The slope is positive on either side of the minima, which suggests that the net force acting upon the system is a restoring one. Similarly, the net force acting on the system at the local maxima is also zero, but this is an unstable equilibrium point. Any movement away from this point results in a force that is acting away from the point.
There will always be a neutral equilibrium point characterized by the constant potential energy regime of the potential energy diagram, where the net force on the system will be zero. Any movement on either side of the neutral equilibrium position will result in a net force on the system, neither restoring nor disrupting.
This text is adapted from <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>.

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

Education

JoVE Core

Unit 1

Potential Energy and Energy Conservation

KEY TERMS AND CONCEPTS

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 local maximum is also an equilibrium point, but it is unstable. The net force at this point is zero. If the system moves away from the top, the force acts farther away from the point.

Potential energy diagrams can also show neutral equilibrium. In this case, the potential energy stays constant over a region, and the net force is zero. A small move to either side still creates a net force, but it is neither restoring nor disruptive.

Stability in Potential Energy Diagrams

gravitational potential energy

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force and potential energy in one dimension

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force and potential energy in three dimensions

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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,...

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...

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Explore how potential energy diagrams reveal stable, unstable, and neutral equilibrium points, including local minima, maxima, and zero net force.

Stability in Potential Energy Diagrams | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Pennsylvania State Academic Standards

Physical Science

3.2.9-12.S

Louisiana Student Standards for Science

High School

Chemistry

HS-PS3-4

HS-PS3-5

Tennessee Academic Standards

PHYS.PS3.3

PHYS.PS3.8

CHEM1.PS3.4

Virginia  Standards of Learning

HIgh School

PH.4

PH.4.b

Alabama Course of Study Science

9-12.PS.1.1

9-12.P.2.3.b

Next Generation Science Standards

HS-PS3-2

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.C

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-2.

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Stability in Potential Energy Diagrams

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