Name: work-energy along curved paths
Uploaded: 2023-05-16T08:18:40.000Z
Duration: 1 min 9 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-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

Bir cismi eğri bir yol boyunca yer değiştirmek için yapılan iş, cismin kinetik enerjisindeki değişime eşittir. Bu iş-enerji teoremidir.
Başlangıçta hareketsiz halde olan ihmal edilebilir kütleli bir ipe bağlı bir top düşünün. Top düştüğünde, dairesel bir yol izleyerek sallanır.
Topa yolu üzerindeki herhangi bir rastgele noktada etki eden kuvvetleri anlamak için bir serbest cisim diyagramı çizilebilir.
Yapılan iş, kuvvet bileşeninin çarpımının yer değiştirme ve yer değiştirme boyunca entegre edilmesiyle bulunabilir.
Kuvvet ve yer değiştirmeyi açısal yer değiştirmenin bir fonksiyonu olarak koyarak ve ifadeyi başlangıçtan son konuma entegre ederek, yapılan işin ifadesi elde edilir.
İş, topun kinetik enerjisindeki değişime eşittir.
Top başlangıçta hareketsiz olduğu için ilk kinetik enerjisi sıfırdır. Bu nedenle, en düşük noktadaki son kinetik enerji, topun başlangıç konumundaki potansiyel enerjisi ile aynıdır.

<ol>
	<li>Genç, H.D ve Freedman, R.A. (2012). Modern Fizik ile Üniversite Fiziği. San Francisco, CA: Pearson: bölüm 6.3; sayfa 191–192.</li>
</ol>

eğri boyunca hareket İçin İş-enerji teoremi

İş-enerji teoremi, bir parçacığın herhangi bir eğri yol boyunca hareketi için genelleştirilebilir. Basit bir argüman burada şudur: eğri yol, birçok sıfır büyüklüğündeki yolun toplamı olarak düşünülebilir ve her biri düz bir yol olabilir. Parçacıktaki kuvvet, böyle bir sıfır büyüklüğündeki yol boyunca sabit kabul edilebilir, bu nedenle iş-enerji teoremi uygulanabilir. Bu yolların toplamı için de geçerlidir. Net yapılan iş, sıfır büyüklüğündeki yollar boyunca yapılan işin integralidir ve toplam kinetik enerji değişimi tüm değişikliklerin toplamıdır.

Dikkat edilmesi gereken nokta, eğri bir yol boyunca hareket için kuvvetin zorunlu olarak eğri boyunca olmamasıdır. Yani, kuvvet iki bileşene sahip olabilir: eğrinin tangenti boyunca bir bileşen ve tangente dik olan bir bileşen. Parçacık üzerinde iş yapan ve bu nedenle kinetik enerjisini değiştiren kuvvet, tangansiyel kuvvettir. Kuvvetin ve sıfır büyüklüğündeki çizgi elemanının nokta çarpımının çizelgeye verdiği iş, lineer integraldir.

Eğri Boyunca Hareket İçin İş-Enerji Teoremi

İş-enerji teoremi, bir parçacığın herhangi bir eğri yol boyunca hareketine genelleştirilebilir. Buradaki basit argüman, eğri yolun ...

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Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Work and Kinetic Energy

İş ve Kinetik Enerji

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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.

For curved motion, the force may not point along the curve. It can be split into two components: one tangent to the curve and one perpendicular to the tangent. Only the tangential force does work on the particle and changes its kinetic energy. The work is written as a line integral of the dot product of the force and the infinitesimal line element.

Work-Energy Along Curved Paths

work

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...

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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

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Work Done and Kinetic Energy

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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

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.

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

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work done by gravity

Gravity and Positive vs Negative Work

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power

Power in Work and Motion

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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 the work-energy theorem applies to curved paths, why the path is split into tiny straight segments, and how tangential force changes kinetic energy.

Work-Energy Along Curved Paths | JoVE K12

physics

JoVE Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

PS.Phy.6.2

Tennessee Academic Standards

High School

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.11

PHYS.PS3.6

Alabama Course of Study Science

9-12.P.2.3.c

Florida Department of Education

SC.912.P.10

SC.912.P.10.1

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-PS3-1.

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Mechanisms of Heat Transfer I

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Mechanisms of Heat Transfer II

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conduction-convection-and-radiation-problem-solving

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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 ...

Conservation of Mechanical Energy

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 ...

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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

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Conservation of Energy

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Conservation of Energy: Application

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

PS.PSc.7.2

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

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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 ...

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 ...

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 ...

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 ...

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.
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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.

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.

Work-Energy Along Curved Paths

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