Name: kinetic energy, momentum, and reference frames
Uploaded: 2023-04-30T10:56:07.000Z
Duration: 56 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Physical Science

Energy

3.2.9-12.P

Kinetic Energy - II

The kinetic energy of an object is defined as one half of the product of mass and velocity squared with the units kilograms meter squared per second squared.
The kinetic energy of an object can be calculated using the momentum equation. The velocity term in the equation can be substituted from the momentum expression. Thereby, obtaining a relationship between momentum, mass, and kinetic energy of the object.
The kinetic energy of an object depends on the frame of reference in which it is measured.
For example, consider a person sitting in a car moving at a constant velocity. Since the person is stationary, his kinetic energy with respect to another stationary person sitting in the same car is zero. While, for an observer standing outside, it is non zero.

kinetic energy - ii

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s second law can be expressed as either the rate of change of momentum or mass multiplied by the rate of change of velocity, so too can the kinetic energy of a particle be expressed in terms of its mass and momentum, instead of its mass and velocity. 
<img alt="Kinetic energy equation \(K = \frac{p^2}{2m}\), physics formula analysis." src="/files/ftp_upload/12667/12667_Equation_1.png" style="text-align: center; height: 35px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
In the equation, the units of kinetic energy are mass times the speed-squared, or
<img alt="Physics: SI unit for energy (joule) formula; symbol kg&#183;m&#178;/s&#178;; mathematical notation." src="/files/ftp_upload/12667/12667_Equation_2.png" style="text-align: center; height: 20px;" data-altupdatedat="1761830439000" data-alt="Figure2" />
Note that the units of force are mass multiplied by acceleration. Thus, the units of kinetic energy are also the units of force multiplied by distance, which are the units of work, or joules. Hence, work and kinetic energy have the same units, since they are different forms of the same, more general, physical property.
Because velocity is a relative quantity, the value of kinetic energy depends on the frame of reference. One can generally choose a frame of reference that is suited to the purpose of analysis and that simplifies the calculations. One such frame of reference is the one in which the observations of the system are made (likely an external frame). Another choice is a frame that is attached to or moves with the system (likely an internal frame).
This text is adapted from <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>

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Education

JoVE Core

Physics

Unit 1

Work and Kinetic Energy

KEY TERMS AND CONCEPTS

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 forms of the same, more general physical property.

Velocity is relative, so kinetic energy is relative too. Its value depends on the frame of reference used for analysis. A common choice is the frame where the observations are made, which is usually an external frame. Another option is a frame attached to the system or moving with it, which is usually an internal frame. Choosing the right frame can simplify the calculation.

Kinetic Energy, Momentum, and Reference Frames

kinetic-energy-momentum-and-reference-frames

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 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

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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...

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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

Explore how kinetic energy relates to mass, speed, momentum, work, and reference frames. Learn why the same energy can be measured in joules.

Kinetic Energy, Momentum, and Reference Frames | 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.

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

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New Jersey Student Learning Standards for Science

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

Types of Potential Energy

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Elastic Potential Energy

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Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

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

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Force and Potential Energy in One Dimension

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Force and Potential Energy in Three Dimensions

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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

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3.2.9-12.S

Kinetic Energy, Momentum, and Reference Frames

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