Name: variable force work via graphs and energy
Uploaded: 2025-05-22T09:06:08.000Z
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

Physical Science

Energy

PS.PSc.7.3

Work and Energy for Variable Forces

Değişken hızda hareket eden bir araba, değişken bir kuvvetin etkisi altındadır.
Arabayı A noktasından B noktasına hareket ettirirken kuvvetin yaptığı işi bulmak için, arabanın kat ettiği mesafe ile tek boyutlu değişen kuvvet çizilir.
Eğrinin altındaki alan, ayrı genişlikte bir dizi şeride bölünmüştür.
Her şerit için uygulanan kuvvet yaklaşık olarak sabittir.
Bu nedenle, A ve B arasındaki toplam mesafe için değişken kuvvet tarafından yapılan iş, küçük segmentler için sabit kuvvet tarafından yapılan bireysel işin toplamı ile verilir.
Daha iyi bir yaklaşım için, şerit sayısını, her şeridin genişliği sıfıra yaklaşacak şekilde artırın. Böylece yapılan iş, mesafeye göre tek boyutlu değişen kuvvetin integrali ile verilebilir ve eğrinin altındaki alan olarak temsil edilebilir.
Newton'un ikinci yasasını kullanarak ve kalkülüsün zincir kuralını uygulayarak, yapılan iş, iş-enerji teoremi olan kinetik enerjideki değişim açısından yeniden yazılabilir.

<ol>
	<li>Genç, H.D ve Freedman, R.A. (2012). Modern Fizik ile Üniversite Fiziği. San Francisco, Kaliforniya: Pearson. Sayfa 187-190</li>
	<li>Walker J. Halliday ve Resnick, 10. baskı. Fiziğin Temelleri: Wiley. Sayfa 162-164</li>
</ol>

değişken güçler için Çalışma ve enerji

Bir nesne değişken bir güç tarafından etkilendiğinde, yapılan işin miktarı ve nesnenin enerjideki değişimi, sabit bir güç uygulandığında hesaplamak kadar karmaşık olabilir. İş, kuvvet ile yer değiştirmenin çarpımıyken enerji ise bir sistemin iş yapma kapasitesidir. Bir nesneye sabit bir kuvvet uygulandığında yapılan iş, kuvvetle kuvvetin etki yönünde hareket ettiği mesafe arasındaki çarpım olarak hesaplanabilir. Ancak değişken bir kuvvet uygulandığında, yapılan iş kuvvet-deplasman grafiğinin altında kalan alan olarak hesaplanır.

Bir nesnenin enerjideki değişimi değişken bir kuvvet uygulandığında hesaplamak daha karmaşık olabilir. Bu durumda, iş-enerji prensibi kullanılabilir. Bu prensip, bir nesne üzerinde yapılan işin, kinetik enerjisindeki değişiminin ve potansiyel enerjisindeki değişiminin toplamına eşit olduğunu belirtir. Bu nedenle, bir nesnenin toplam enerjideki değişimi, kinetik ve potansiyel enerjisindeki değişikliklerini ekleyerek hesaplanabilir.

Bir nesneye değişken bir kuvvet uygulandığında, yapılan işin miktarı ve nesnenin enerjideki değişimi, matematiksel analiz yöntemleri ve iş-enerji prensibi kullanılarak hesaplanabilir. Bu kavramların anlaşılması, değişken kuvvetlerin nesneler üzerindeki etkilerinin sık sık karşılaşıldığı fizik ve mühendislik gibi birçok alanda önemlidir.

Kinetik enerjideki değişimi hesaplamak için bir nesneye uygulanan işin, değişken kuvvetler için de geçerli olan iş-enerji teoremi kullanılabilir. Bu, bir kuvvetin sabit veya zamanla değişse de, bir nesne üzerinde yapılan işin, kuvvetin kat edilen mesafeyi entegre ederek hesaplanabileceği ve bu işin nesnenin kinetik enerjisinde bir değişikliğe neden olduğu anlamına gelir.

Örneğin, bir nesne değişen bir kuvvetle itildiğinde, nesne üzerindeki toplam iş, nesnenin itildiği mesafe boyunca kuvvetin entegre edilmesiyle bulunabilir. Bu iş, bir nesnenin kinetik enerjisinde bir değişikliğe neden olur ve bu kinetik enerji iş-enerji teoremi kullanılarak hesaplanabilir. Bu nedenle, iş-enerji teoremi, değişken kuvvetlere maruz kalan nesnelerin hareketini analiz etmek için kullanılabilecek güçlü bir araçtır.

Değişken Güçler için Çalışma ve Enerji

Bir cisme değişken bir kuvvet etki ettiğinde, yapılan iş miktarı ve cismin enerjisindeki değişimin hesaplanması karşılaştırıldığında daha karmaşık olabilir...

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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

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 graph. This graph-based method helps show how much work is done when the force is not the same at every point.

The change in energy can also be analyzed with the work-energy principle. This principle says that the work done on an object equals its change in kinetic energy plus its change in potential energy. The total change in energy is found by adding the changes in kinetic and potential energy.

The work-energy theorem also applies when forces vary. It states that the work done on an object equals its change in kinetic energy. In practice, the work can be found by integrating the force over the distance traveled. If an object is pushed with a varying force, this method gives the total work and the resulting change in kinetic energy. These ideas are useful in physics and engineering, where variable forces are common.

Variable Force Work via Graphs and Energy

variable-force-work-via-graphs-and-energy

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...

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...

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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...

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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 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...

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 variable forces affect work and energy using force-displacement graphs, the work-energy principle, and the work-energy theorem in high school physics.

Variable Force Work via Graphs and Energy | 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

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

South Carolina College and Career Ready Science Standards

P-PS3-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-1.

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Conservation of Mechanical Energy

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Conservative Forces

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Non-conservative Forces

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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

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 ...

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 ...

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 ...

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

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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.

Variable Force Work via Graphs and Energy

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