Name: work in physics: force and motion
Uploaded: 2023-04-30T10:55:37.000Z
Duration: 1 min 22 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.7.3

Work

仕事は、力を加えることによってエネルギーが一つのエンティティから別のエンティティに転送されるときに行われると言われています。たとえば、力Fがボックスに適用され、変位dsを通過すると、摩擦力に逆らって作業が行われます。
プロセス中に行われる作業の増分は、力ベクトルと変位ベクトルの内積に等しくなります。
オブジェクトの変位に平行に加えられる力の成分のみが、行われる作業に貢献します。
オブジェクトが位置AからBに移動されたとき、力によって行われる総仕事は、変位の経路に沿った変位に対する力の積分です。
大きさと方向の両方で一定の力の場合、積分は端点のみに依存するため、実行される作業は経路に依存しません。
ばねの膨張や圧縮など、可変の力が物体に作用している場合、ばねの力は距離の関数として表されます。初期位置から最終位置への変位に沿ったばね力によって行われる仕事は、この式で与えられます。ここで、kはばね定数です。

仕事

仕事は、エネルギーが 1 つの物体から別の物体に伝達されるときに行われます。 言い換えれば、仕事とは、何かに力が作用して、ある位置から別の位置に変位することです。 力は位置の関数として変化する可能性があり、変位は 2 点間のさまざまな経路に沿って発生する可能性があります。 微小な変位を通じて作用する力によって行われる仕事の増分 (dW) は、力のドット積 (<img alt="Image1" src="/files/ftp_upload/12663/12663img01.png" />) およびディスプレイスメント (<img alt="Image1" src="/files/ftp_upload/12663/12663img02.png" />) ベクトル。

ドット積は、ベクトルの大きさとベクトル間の角度のコサインで表すことができます。これは、ドット積を大きさと角度の表現として言葉で定義する方が簡単だからです。 ベクトルのレッスンで紹介したように、さまざまなコンポーネントの観点から表現することもできます。

ベクトルのプロパティから、変位に平行な力の成分を取得するか、力に平行な変位の成分を取得するかは問題ではありません。結果はどちらでも同じです。 仕事の単位は、力の単位に長さの単位を乗じたものです。 これは、SI 系におけるニュートンとメートル (N·m) の積です。 イギリスの系では、力の単位はポンド (lb)、距離の単位はフィート (ft) であるため、仕事の単位はフィートポンド (ft·lb) となります。

大きさと方向が一定の力によって行われる仕事は、計算が最も簡単です。 一般に、力は空間内の各点で大きさと方向が異なり、2 点間の経路が曲がることがあります。 可変の力によって行われる微小な仕事は、力の成分と経路に沿った変位の観点から表現できます。 このような場合、力の成分は経路に沿った位置の関数であり、変位は経路の方程式に依存します。 ただし、仕事の物理的な概念は単純です。小さな変位の仕事を計算し、それらを合計します。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/7-1-work"> から編集されたものです。 Openstax, University Physics Volume 1, Section 7.1: Work.</a>

仕事は、エネルギーが1つのオブジェクトから別のオブジェクトに転送されるときに行われます。言い換えれば、仕事とは、変位を受ける何かに力が作用するときです...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Work and Kinetic Energy

仕事と運動エネルギー

KEY TERMS AND CONCEPTS

主要用語と概念

work in physics: force and motion

Work in physics connects force, motion, and energy transfer. Work is done when a force acts on an object and that object moves from one position to another. If there is no displacement, no work is done, even if a force is present.

The amount of work depends on the force and the direction of motion. For a very small displacement, the work done is written as the dot product of force and displacement vectors. That means work depends on the size of the vectors and the angle between them. You can also describe it using vector components, and it gives the same result whether you use the force component along the displacement or the displacement component along the force.

Work is measured in units of force times distance. In the SI system, that unit is the newton-meter, or N·m. In the English system, it is the foot-pound, or ft·lb.

The easiest case is a force that stays constant in both size and direction. In more general situations, the force can change from place to place, and the path between two points can be curved. Then the work is found by adding the tiny work done over each small part of the path. The force components and the path equation both matter in those cases, but the main idea stays the same: break the motion into small steps and add the work from each one.

Work in Physics: Force and Motion

work

Work in physics connects force, motion, and energy transfer. Work is done when a force acts on an object and that object moves from one position to another. If there is no displacement, no work is done, even if a force is present. The amount of work depends on the force and the direction of motion. For a very small displacement, the work done is written as the dot product of force and displacement vectors. That means work depends on the size of the vectors and the angle between them. You can...

positive, negative, and zero work

How Force Direction Changes Work

Work in physics depends on the direction of a force and the way an object moves. Work is done when energy is transferred to an object. It happens when a force acts on a body that moves from one position to another. The work done by a force is defined as the integral of the force with respect to displacement along the path. Forces can change with position, and an object can move along different paths between the same two points. In vector form, the size of a force times the cosine of the angle...

energy

Energy Sources and Forms in Matter

Energy in matter comes from the Sun and changes form in many everyday processes. The universe is made of matter in different forms, and all forms of matter contain energy. On Earth, many energy sources can be traced back to the Sun, which is the ultimate energy source. Plants capture light energy from the Sun during photosynthesis and convert it into chemical energy. This stored energy can then be used in several ways. People get energy from plant foods, and wood or coal, which are fossilized...

types of potential energy

Potential Energy Examples in Everyday Physics

Potential energy is stored energy, and it appears in several everyday forms. It is also called energy at rest because it is ready to be used later. In physics, different systems can store energy in different ways. Gravitational potential energy is the energy stored by an object because of its position. An apple hanging from a tree is one clear example. Electrical potential energy is stored when electric charges attract or repel each other. Chemical potential energy is stored in the bonds...

types of kinetic energy

How Mass and Speed Affect Kinetic Energy

Kinetic energy depends on an object’s mass and speed. A heavier object moving at the same speed has more kinetic energy than a lighter one. An object moving faster also has more kinetic energy when the mass stays the same. The transcript also describes several forms of kinetic energy. Mechanical energy is linked to the motion of an object. A bullet fired from a gun and water flowing down a dam are examples of mechanical energy. Electrical energy comes from the flow of electric charges.

kinetic energy - i

Motion Energy in Collisions

Kinetic energy is the energy of motion. It depends on how fast an object moves, not on the direction of its velocity. In classical mechanics, this idea helps explain how moving bodies affect other bodies during collisions. A classic example is a perfectly elastic, head-on collision between two identical bodies, with one body initially at rest. After the collision, the first body stops, and the second body moves away with the first body's original velocity. This same pattern can be seen in...

kinetic energy - ii

Kinetic Energy, Momentum, and Reference Frames

Kinetic energy depends on mass, speed, momentum, and the frame of reference. For a particle, it is one-half of the particle’s mass times the square of its speed. The same idea can also be written in terms of mass and momentum instead of mass and velocity. The units of kinetic energy are mass times speed-squared. These units match the units of work. Force times distance also gives the same units, so kinetic energy and work are measured in joules. That is why work and kinetic energy are two...

work-energy theorem

Work Done and Kinetic Energy

Work done by the net force is linked to an object's kinetic energy. In physics, the net force is the total force acting on an object. Kinetic energy is the energy of motion. The work-energy theorem states that the work done by all forces on an object equals the change in its kinetic energy. This relationship is useful when acceleration is not constant. If the change in velocity is known, the theorem can still help calculate the work done by a force. It connects force, motion, and energy in a...

work and energy for variable forces

Variable Force Work via Graphs and Energy

Variable force work and energy can be found by using force-displacement graphs and the work-energy principle. When a force changes as an object moves, the calculation is more complex than for a constant force. Work is the product of force and displacement, and energy is the capacity of a system to do work. For a constant force, work is found by multiplying the force by the distance moved in the direction of the force. For a variable force, the work done is the area under the force-displacement...

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work-energy theorem for motion along a curve

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

Work-Energy Along Curved Paths

The work-energy theorem can be applied to motion along a curved path. A curved path can be treated as many tiny straight paths added together. On each small part, the force can be taken as constant, so the work-energy theorem can be used there. The total result comes from adding the work done along all of those small path segments. The net work is found with an integral, which adds the work from each infinitesimal path. The total change in kinetic energy is the sum of the changes along the way.

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work done over an inclined plane

Gravity and Work on Sloped Motion

Gravity and work on sloped motion can be described with the center-of-mass framework. For a rigid body, internal forces do no work, so they can be ignored. The work-energy theorem then uses only the external forces. The work done by gravity depends on the path of the body’s center of mass. If gravity helps increase kinetic energy, the work is positive. If an object is lifted against gravity, the work is negative because kinetic energy decreases. For horizontal motion, the work done by or...

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work done by many forces

Calculating Work from Multiple Forces

Calculating work from multiple forces can be done in two ways, and both methods give the same result. One method finds the work done by each force first. The other method finds the net force by adding the force vectors first.

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work done by gravity

Gravity and Positive vs Negative Work

Gravity is one of the four fundamental forces in nature. On Earth, the force between an object and Earth is called gravity. Gravity does work on an object when it moves the object toward Earth’s center. In that case, the work done by gravity is positive. When an external force lifts an object away from Earth’s center, that force works against gravity. The net work done in this case is negative. If an object moves along the Earth with no change in distance toward or away from Earth’s center,...

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power

Power in Work and Motion

Power connects work with the time needed to do it. Work depends on force and displacement. The work-energy theorem also links net work on an object to the change in its kinetic energy between two points on its path. These ideas do not include time directly, but time still matters in many real situations. A sprinter is a clear example. Two runners may reach the same finish speed, so they do the same amount of work. The winner is the one who reaches that speed in less time. Power describes this...

power expended by a constant force

Power as the Rate of Doing Work

Power describes how fast work is done. In physics, two sprinters can cross the finish line with the same velocity and do the same amount of work, but the one who finishes first has greater power because the work takes less time. Average power is the work done during a time interval divided by that time interval. When the time interval becomes very small, this becomes instantaneous power. That gives the power at a specific moment instead of over a longer stretch of time. Power can also be...

key terms and concepts

Learn how work links force, displacement, and energy transfer. See how dot products, vector components, and units like N·m and ft·lb apply.

Work in Physics: Force and Motion | 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.PSc.7.4

PS.Phy.6.2

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

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

Transfer and transformation of energy (including work)

Work and power

Virginia  Standards of Learning

HIgh School

PH.4

PH.4.b

Arizona Science Standards

High School

HS.P4

HS.P4U1.8

HS+Phy.P4

HS+Phy.P4U1.6

HS.P4U3.9

Alabama Course of Study Science

9-12.PS.1.1.a

9-12.P.2.3.a

9-12.P.2.3.c

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.A

Georgia Standards of Excellence

SPS8.

Work and Simple Machines

SP3.

Work-Kinetic Energy Theorem.

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PS.PSc.7.2

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Work-Energy Theorem for Motion Along a Curve

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Work Done Over an Inclined Plane

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Work Done by Many Forces

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Power

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Work in Physics: Force and Motion

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