Name: motion energy in collisions
Uploaded: 2023-04-30T10:55:59.000Z
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K12 Standards

Pennsylvania State Academic Standards

9-12

Physical Science

Energy

3.2.9-12.P

Kinetic Energy - I

A energia que um objeto possui em virtude de seu movimento é conhecida como energia cinética. Se um objeto está se movendo com uma velocidade v, sua energia cinética é definida como metade do produto da massa e da velocidade ao quadrado.
A velocidade ao quadrado aqui é o produto escalar do vetor velocidade consigo mesmo. Portanto, a energia cinética é uma grandeza escalar, pois é independente da direção do movimento e depende apenas da velocidade do objeto.
A massa e a velocidade ao quadrado nunca podem ser negativas. Portanto, a energia cinética possuída por um objeto é sempre positiva e aumenta rapidamente com o aumento da velocidade.
Por exemplo, se duas bolas de boliche com massas diferentes estão se movendo com a mesma velocidade, a segunda bola de boliche, devido à sua massa dupla, tem o dobro da energia cinética.
Se a velocidade da bola mais leve for dobrada, sua energia cinética é aumentada quatro vezes. Se a massa ou a velocidade de um objeto forem insignificantes, sua energia cinética será zero.

energia cinética - i

É plausível supor que quanto maior for a velocidade de um corpo, maior será o efeito que ele pode ter sobre outros corpos. Isso não depende da direção da velocidade, apenas da sua magnitude. No final do século XVII, uma quantidade foi introduzida na mecânica para explicar colisões entre dois corpos perfeitamente elásticos, nos quais um corpo colide de frente com um corpo idêntico em repouso. Quando colidem, o primeiro corpo para e o segundo corpo se afasta com a velocidade inicial do primeiro corpo. Se você já jogou bilhar ou croquet, ou já viu um pêndulo de Newton, você terá observado esse tipo de colisão. A ideia por trás dessa quantidade estava relacionada às forças atuando em um corpo e era referida como "a energia do movimento". Mais tarde, durante o século XVIII, foi dado o nome de energia cinética para a energia do movimento.

Com isso em mente, temos a definição clássica de energia cinética. Note que quando falamos "clássica", queremos dizer não-relativística; ou seja, em velocidades muito inferiores à velocidade da luz. Em velocidades comparáveis à velocidade da luz, a teoria especial da relatividade requer uma expressão diferente para a energia cinética de uma partícula.

As unidades de energia cinética são a massa multiplicada pelo quadrado da velocidade (kg·m²/s²). As unidades de força são a massa multiplicada pela aceleração (kg·m/s²), então as unidades de energia cinética também são as unidades de força multiplicadas pela distância. Essas são as unidades de trabalho, ou joules.

A energia cinética de uma partícula é uma única quantidade, mas a energia cinética de um sistema de partículas às vezes pode ser dividida em vários tipos, dependendo do sistema e dos seus movimentos. Por exemplo, se todas as partículas em um sistema têm a mesma velocidade, o sistema está passando por um movimento translacional e possui energia cinética translacional. Se um objeto está girando, ele pode ter energia cinética rotacional. Se um objeto está vibrando, ele pode ter energia cinética vibracional. A energia cinética de um sistema, em relação a um referencial interno, é chamada de energia cinética interna. A energia cinética associada ao movimento molecular aleatório é chamada de energia térmica. Esses nomes serão usados em capítulos posteriores, quando apropriado. Independentemente do nome, todos os tipos de energia cinética são a mesma quantidade física, representando a energia associada ao movimento.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy">Openstax, University Physics Volume 1, Section 7.2: Kinetic Energy.</a>

Energia Cinética - I

É plausível supor que quanto maior a velocidade de um corpo, maior o efeito que ele poderia ter sobre outros corpos. Isso não depende do ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Work and Kinetic Energy

Trabalho e Energia Cinética

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 billiards, croquet, and a Newton's cradle.

The term was first tied to the idea of the energy of motion and later named kinetic energy in the eighteenth century. Here, classical means non-relativistic, so it applies at speeds much slower than the speed of light. At speeds near the speed of light, special relativity requires a different expression for kinetic energy.

The units of kinetic energy are mass times speed squared, or kg·m²/s². These units are the same as force times distance, which are the units of work. That is why kinetic energy is measured in joules.

For a system of particles, kinetic energy can take different forms based on the motion of the system. If all the particles share the same velocity, the system has translational kinetic energy. Rotating objects can have rotational kinetic energy, and vibrating objects can have vibrational kinetic energy.

Kinetic energy can also be described relative to an internal frame of reference, where it is called internal kinetic energy. The kinetic energy linked to random molecular motion is called thermal energy. Even with different names, each type still represents energy associated with motion.

Motion Energy in Collisions

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

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 kinetic energy explains collisions, motion, and energy units. See examples like billiards, Newton's cradle, rotation, vibration, and thermal energy.

Motion Energy in Collisions | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

3.2.9-12.Q

Louisiana Student Standards for Science

High School

HS-PS3-2

HS-PS3-3

HS-PS3-1

Tennessee Academic Standards

PHYS.PS3.1

Minnesota Academic Standards in Science

2.2.1 9P.2.2.1.1

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Arizona Science Standards

HS+Phy.P4

HS+Phy.P4U1.6

Next Generation Science Standards

Florida Department of Education

SC.912.P.10

SC.912.P.10.1

SC.912.P.12

SC.912.P.12.9

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.B

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South Carolina College and Career Ready Science Standards

P-PS3-1

P-PS3-2

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New York State Science Learning Standards

HS. Energy

HS-PS3-1.

Georgia Standards of Excellence

SP3.

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3.2.9-12.O

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Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Elastic Potential Energy

Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is ...

Energy in Simple Harmonic Motion

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Kinetic and Potential Energy of a Wave

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Energy and Power of a Wave

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Energy Carried By Electromagnetic Waves

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Students who demonstrate understanding can develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects). Clarifying Statement: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations. Assessment Boundry: N/A

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Energy Transfer in Chemical Reactions

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Students who demonstrate understanding can design, build and refine a device that works within given constraints to convert one form of energy into another form of energy. Clarifying Statement: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. Assessment Boundry: Assessment for quantitative evaluations is limited to total output for a given input. Assessment is limited to devices constructed with materials provided to students.

Students who demonstrate understanding can plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). Clarifying Statement: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. Assessment Boundry: Assessment is limited to investigations based on materials and tools provided to students.

3.2.9-12.R

force-and-potential-energy-in-one-dimension

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular ...

force-and-potential-energy-in-three-dimensions

Force and Potential Energy in Three Dimensions

Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function ...

Energy Diagrams - I

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the ...

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the ...

Students who demonstrate understanding can develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. Clarifying Statement: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other. Assessment Boundry: Assessment is limited to systems containing two objects.

3.2.9-12.S

Motion Energy in Collisions

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