Name: power as the rate of doing work
Uploaded: 2023-04-30T10:56:30.000Z
Duration: 57 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

NC K-12 Science Standard Course of Study

9-12

Physical Science

Energy

PS.PSc.7.4

Power Expended by a Constant Force

Moc to tempo, w jakim praca jest wykonywana. Wzór na moc można przegrupować, aby uzyskać wykonaną pracę, jeśli znana jest moc wyjściowa podczas procesu.
Jeśli moc wyjściowa zmienia się w funkcji czasu, praca wykonana jest całką mocy w tym okresie, a zatem obszar pod krzywą daje wartość wykonanej pracy.
Kiedy na obiekt przyłożona jest stała siła, moc obiektu można wyrazić w postaci działającej na niego siły i przemieszczenia pokrytego przez obiekt. Tutaj pochodną przemieszczenia w czasie jest prędkość. W ten sposób moc może być również reprezentowana jako iloczyn siły i prędkości.
Z równania moc może być dodatnia, ujemna lub zerowa w zależności od kąta między siłą a wektorem prędkości.

moc wydatkowana przez stałą siłę

Zależność pomiędzy wykonaną pracą a czasem potrzebnym na jej wykonanie można wyjaśnić za pomocą pojęcia mocy. Na przykład kilku sprinterów biorących udział w wyścigu może mieć tę samą szybkość, gdy dotrą do mety, wykonując w ten sposób tę samą ilość pracy, ale zwycięzca zrobi to w najkrótszym czasie. Zatem moc definiuje się jako szybkość wykonywania pracy. Ponieważ praca może zmieniać się w funkcji czasu, moc średnią definiuje się jako pracę wykonaną w przedziale czasu podzieloną przez ten przedział czasu. Moc średnią nazywa się mocą chwilową, gdy przedział czasu jest bliski zeru.

Moc związaną z poruszaniem ciała można również wyrazić w kategoriach sił działających na ciało. Jeśli na ciało przemieszczone ds w czasie dt działa siła F, moc wydatkowana przez tę siłę wynosi

<img alt="Figure1" src="/files/ftp_upload/12670/12670_Equation_1.png" style="text-align: center; height: 40px;" />

gdzie v to prędkość ciała. Fakt, że istnieją granice ruchu ciała rzeczywistego wynikające z pochodnych, uzasadnia przegrupowanie nieskończenie małych.

Ten tekst jest adaptacją <a href="https://openstax.org/books/university-physics-volume-1/pages/7-4-power"> Openstax, University Physics, tom 1, sekcja 7.4: Moc.</a>

Moc wydatkowana przez stałą siłę

Zależność między wykonaną pracą a czasem potrzebnym na jej wykonanie można wyjaśnić za pomocą pojęcia władzy. Na przykład kilku sprinterów w wyścigu może ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Work and Kinetic Energy

Praca i energia kinetyczna

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 written in terms of force and motion. If a force F acts on a body and the body moves a small distance ds in a time dt, the power expended by the force can be written using the body's velocity v. This relationship follows from the way work and time change for a real moving body.

Power as the Rate of Doing Work

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...

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...

/files/media/science-education/science-education-thumbs/14701.jpg

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.

/files/media/science-education/science-education-thumbs/14735.jpg

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,...

/files/media/science-education/science-education-thumbs/14750.jpg

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 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

Explore how power in physics depends on time, work, and motion. Learn the difference between average power, instantaneous power, and force-based power.

Power as the Rate of Doing Work | 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.Phy.6.2

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Work and power

Tennessee Academic Standards

High School

PHYS.PS3.6

Alabama Course of Study Science

9-12.P.2.3.a

Florida Department of Education

SC.912.P.10

SC.912.P.10.3

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.A

Georgia Standards of Excellence

SP3.

Power

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PS.PSc.7.1

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Types of Potential Energy

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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 ...

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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 ...

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 ...

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

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.

PS.PSc.7.3

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 ...

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.

Analyze energy transfers and transformations within a mechanical system.

Power as the Rate of Doing Work

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