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

Man spricht von Arbeit, wenn Energie durch Kraftanwendung von einer Entität auf eine andere übertragen wird. Wenn z. B. eine Kraft F auf einen Kasten ausgeübt wird und er sich durch eine Verschiebung ds bewegt, wird gegen die Reibungskraft gearbeitet.
Das Inkrement der während des Prozesses geleisteten Arbeit ist gleich dem Punktprodukt der Kraft- und Verschiebungsvektoren.
Nur die Kraftkomponente, die parallel zur Verschiebung des Objekts ausgeübt wird, trägt zur geleisteten Arbeit bei.
Wenn ein Objekt von Position A nach B bewegt wird, ist die gesamte von der Kraft geleistete Arbeit das Integral der Kraft in Bezug auf die Verschiebung entlang des Weges der Verschiebung.
Bei einer Kraft, die sowohl in der Größe als auch in der Richtung konstant ist, hängt das Integral nur von den Endpunkten ab, und daher ist die geleistete Arbeit unabhängig vom eingeschlagenen Weg.
Wenn eine variable Kraft auf ein Objekt wirkt, wie z. B. die Ausdehnung oder Kompression einer Feder, wird die Federkraft als Funktion des Abstands ausgedrückt. Die Arbeit, die die Federkraft entlang der Verschiebung von der Ausgangsposition zur Endposition leistet, wird durch diese Gleichung gegeben, wobei k die Federkonstante ist.

arbeit

Arbeit wird verrichtet, wenn Energie von einem Objekt auf ein anderes übertragen wird. Mit anderen Worten, Arbeit findet statt, wenn eine Kraft auf etwas wirkt, das eine Verschiebung von einer Position zur anderen durchläuft. Kräfte können in Abhängigkeit von der Position variieren und Verschiebungen können entlang verschiedener Pfade zwischen zwei Punkten erfolgen. Die Zunahme der Arbeit (dW), die von einer Kraft bei einer infinitesimalen Verschiebung verrichtet wird, kann als Skalarprodukt von Kraft (F) und Verschiebung (dX) definiert werden.

Das Skalarprodukt kann in Bezug auf die Beträge der Vektoren und den Kosinus des Winkels zwischen ihnen ausgedrückt werden, da es einfacher ist, das Skalarprodukt in Worten als Ausdruck von Beträgen und Winkeln zu definieren. Es kann auch in Bezug auf verschiedene Komponenten ausgedrückt werden, wie im Vektor-Lektionsmaterial eingeführt.

Aus den Eigenschaften von Vektoren spielt es keine Rolle, ob Sie die Komponente der Kraft parallel zur Verschiebung oder die Komponente der Verschiebung parallel zur Kraft nehmen - das Ergebnis ist in beiden Fällen dasselbe. Die Einheiten der Arbeit sind Einheiten der Kraft multipliziert mit Einheiten der Länge; dies ist in der SI-Einheit Newton mal Meter (N·m). Im englischen System ist die Einheit der Kraft das Pfund (lb) und die Einheit der Strecke der Fuß (ft), daher ist die Einheit der Arbeit das Fuß-Pfund (ft·lb).

Die von einer konstanten Kraft in Betrag und Richtung verrichtete Arbeit ist am einfachsten zu berechnen. Im Allgemeinen können Kräfte in Betrag und Richtung an verschiedenen Punkten im Raum variieren und die Pfade zwischen zwei Punkten können gekrümmt sein. Die infinitesimale von einer veränderlichen Kraft verrichtete Arbeit kann anhand der Komponenten der Kraft und der Verschiebung entlang des Pfads ausgedrückt werden. In diesen Fällen sind die Komponenten der Kraft Funktionen der Position entlang des Pfads und die Verschiebungen hängen von den Gleichungen des Pfads ab. Die physikalische Vorstellung von Arbeit ist jedoch unkompliziert: Berechnen Sie die Arbeit für winzige Verschiebungen und addieren Sie sie.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/7-1-work">Openstax, University Physics Volume 1, Abschnitt 7.1: Arbeit.</a>

Arbeit

Arbeit ist getan, wenn Energie von einem Objekt auf ein anderes übertragen wird. Mit anderen Worten, Arbeit ist, wenn eine Kraft auf etwas wirkt, das eine Verschiebung erfährt ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Work and Kinetic Energy

Arbeit und kinetische Energie

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 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.

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

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 ...

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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 by Gravity

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Power

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Work in Physics: Force and Motion

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