Name: mechanical energy in isolated systems
Uploaded: 2023-05-16T08:18:40.000Z
Duration: 1 min 5 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

Physical Science

Energy

PS.PSc.7.2

Conservation of Mechanical Energy

重力の影響下で振り子のように前後に揺れるタイヤを考えてみましょう。振り子-地球系は孤立した系であると仮定されています。
振り子が揺れると、システムのエネルギーは重力ポテンシャルエネルギーと運動エネルギーの間で前後に変化しますが、システムの機械的エネルギー(2つの合計)は一定のままです。
振り子が最も低い位置にあるとき、それは最高速度であり、すべてのエネルギーは運動エネルギーです。振り子が瞬間的に停止する最高位置では、速度はゼロであり、すべてのエネルギーは位置エネルギーです。
中間位置では、エネルギーの半分が運動エネルギーで、半分が位置エネルギーです。
孤立したシステムでは、機械的エネルギーの保存則は、システムの総機械的エネルギーが任意の瞬間に一定に保たれると述べています。添え字は、エネルギー伝達プロセス中のさまざまな瞬間を指します。

<ol>
	<li>Walker, J., Halliday, D., Resnick, R. (2007), Fundamentals of Physics, 10th Edition, John Wiley & Sons, Inc.; セクション 8.2; 184-186ページ.</li>
	<li>OpenStaxです。(2019). 大学物理学 Vol.1.【Web版】。<a href="https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy">https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy</a> セクション8.3から取得。372-377ページ。</li>
</ol>

機械エネルギーの保存

系の力学的エネルギー E は、その位置エネルギー U とその系内の物体の運動エネルギー K の合計です。 系内で保存力のみがエネルギー伝達を引き起こす場合、つまり系内の物体に摩擦力や抗力が作用しない場合、この機械エネルギーはどうなるのでしょうか? また、系がその環境から隔離されていると仮定します。 言い換えれば、系の外部の物体からの外力は系内部のエネルギー変化を引き起こしません。

系内の物体に保存力が W 作用する場合、その力は物体の運動エネルギー K と位置エネルギー U の間でエネルギーを伝達します。 系の。 保存力のみがエネルギー変化を引き起こす孤立系では、運動エネルギーと位置エネルギーが変化する可能性があります。 ただし、それらの合計、 系の機械的エネルギーEは変更できません。 この結果は、機械エネルギー保存則と呼ばれます。

機械的エネルギー保存則により、ニュートンの法則だけでは解決するのが難しい問題も解決できます。 系の力学的エネルギーが保存される場合、関係する力によって行われる仕事を見つけることなく、ある瞬間の運動エネルギーと位置エネルギーの合計を別の瞬間のそれらの合計に関連付けることができます。 ニュートンの運動の法則の代わりにエネルギー保存則を使用することの大きな利点は、中間の運動をすべて考慮せずに初期状態から最終状態に移行できることです。

システムの機械的エネルギーEは、その位置エネルギーUと、その中の物体の運動エネルギーKの合計です。これはどうなるのか...

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Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Potential Energy and Energy Conservation

ポテンシャルエネルギーとエネルギー保存の法則

KEY TERMS AND CONCEPTS

主要用語と概念

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 outside the system changes the energy inside it.

When a conservative force does work on an object, it changes how the energy is shared between kinetic and potential forms. The kinetic energy and potential energy can each change. However, their sum, called the mechanical energy E, does not change.

This result is known as the principle of conservation of mechanical energy. It is useful for solving problems that are hard to handle with Newton’s laws alone. Instead of tracking every step of the motion, you can compare the initial and final states and relate the total mechanical energy at one instant to the total at another.

Mechanical Energy in Isolated Systems

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 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...

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...

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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

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

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...

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 kinetic and potential energy shift in an isolated system, why mechanical energy stays constant, and how this principle helps solve physics problems.

Mechanical Energy in Isolated Systems | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

PS.Phy.6.1

Pennsylvania State Academic Standards

3.2.9-12.O

3.2.9-12.R

Louisiana Student Standards for Science

High School

Chemistry

HS-PS3-1

HS-PS3-4

HS-PS3-2

HS-PS3-3

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

Conservation of energy

transfer-and-transformation-of-energy-including-work

Transfer and transformation of energy (including work)

Tennessee Academic Standards

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.11

PHYS.PS3.1

PHYS.PS3.3

PHYS.PS3.8

PHYS.PS3.14

PHYS.PS3.15

CHEM1.PS3.4

Virginia  Standards of Learning

HIgh School

PS.5

PS.5.a

PH.4

PH.4.b

Arizona Science Standards

HS.P4

HS.P4U1.8

Alabama Course of Study Science

9-12.PS.1.1

9-12.PS.1.1.a

9-12.P.2.3

9-12.P.2.3.c

Next Generation Science Standards

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.C

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

South Carolina College and Career Ready Science Standards

C-PS3-4

P-PS3-1

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-3.

Georgia Standards of Excellence

SPS7.

Types of Energy

SP3.

Open and Closed Systems.

Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature ...

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the ...

conduction-convection-and-radiation-problem-solving

Conduction, Convection and Radiation: Problem Solving

There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting ...

Use models to explain thermal energy and its transfer.

PS.PSc.7.1

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 ...

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 mathematics and computational thinking to explain the Law of Conservation of Energy in a mechanical system in terms of kinetic and potential energy.

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 ...

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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 ...

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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 ...

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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

Use mathematics and computational thinking to explain work in terms of the relationship among the applied force to an object, the resulting displacement of the object, and the energy transferred to an object.

PS.PSc.7.3

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 ...

Construct an explanation to infer the relationship between work and power, both quantitatively and qualitatively.

PS.PSc.7.4

Analyze energy transfers and transformations within a mechanical system.

Mechanical Energy in Isolated Systems

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