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written by Tom Henderson
This is a five-part interactive tutorial on the basics of energy in the context of introductory physics. The author presents Work and Energy as a means to analyze the motion of objects, an area of demonstrated weakness among secondary students.  Detailed explanations and sample problems allow students to explore potential, kinetic, and mechanical energy, while also introducing related equations.  Included are force diagrams, quick links to pertinent definitions, and links to animations that allow learners to visualize what is being discussed.  

This item is part of The Physics Classroom, a free online tutorial for high school physics students.
Subjects Levels Resource Types
Classical Mechanics
- Newton's Second Law
= Force, Acceleration
- Work and Energy
= Conservation of Energy
= Work
- High School
- Lower Undergraduate
- Informal Education
- Instructional Material
= Tutorial
- Reference Material
Intended Users Formats Ratings
- Learners
- Educators
- text/html
- image/jpeg
- video/quicktime
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Free access
© 2004 The Physics Classroom
energy, force diagrams, kinetic energy, mechanical energy, potential energy, power, work
Record Cloner:
Metadata instance created November 26, 2007 by Caroline Hall
Record Updated:
April 23, 2014 by Caroline Hall
Last Update
when Cataloged:
November 6, 2006
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Next Generation Science Standards

Disciplinary Core Ideas (K-12)

Definitions of Energy (PS3.A)
  • Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. (6-8)
  • A system of objects may also contain stored (potential) energy, depending on their relative positions. (6-8)
  • Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system's total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (9-12)
Conservation of Energy and Energy Transfer (PS3.B)
  • Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system. (9-12)
  • Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (9-12)
  • Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior. (9-12)
Relationship Between Energy and Forces (PS3.C)
  • When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)

Crosscutting Concepts (K-12)

Energy and Matter (2-12)
  • The transfer of energy can be tracked as energy flows through a natural system. (6-8)
  • The total amount of energy and matter in closed systems is conserved. (9-12)
  • Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of, and within that system. (9-12)
  • Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems. (9-12)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations
  • 6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.
  • 9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.
  • 9-12: 4E/H3. As energy spreads out, whether by conduction, convection, or radiation, the total amount of energy stays the same. However, since it is spread out, less can be done with it.
  • 9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.
  • 9-12: 4E/H10. If no energy is transferred into or out of a system, the total energy of all the different forms in the system will not change, no matter what gradual or violent changes actually occur within the system.

11. Common Themes

11C. Constancy and Change
  • 9-12: 11C/H10. Whatever happens within a system, such as parts exploding, decaying, or reorganizing, some features, such as the total amount of matter and energy, remain precisely the same.

Common Core State Standards for Mathematics Alignments

High School — Number and Quantity (9-12)

Vector and Matrix Quantities (9-12)
  • N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
  • N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

High School — Functions (9-12)

Trigonometric Functions (9-12)
  • F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and use the unit circle to express the values of sine, cosine, and tangent for ?—x, ?+x, and 2?—x in terms of their values for x, where x is any real number.

High School — Geometry (9-12)

Similarity, Right Triangles, and Trigonometry (9-12)
  • G-SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Craft and Structure (6-12)
  • RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11—12 texts and topics.
Range of Reading and Level of Text Complexity (6-12)
  • RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.
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AIP Format
T. Henderson, (2004), WWW Document, (
T. Henderson, The Physics Classroom: Definition and Mathematics of Work, (2004), <>.
APA Format
Henderson, T. (2006, November 6). The Physics Classroom: Definition and Mathematics of Work. Retrieved February 24, 2018, from
Chicago Format
Henderson, Tom. The Physics Classroom: Definition and Mathematics of Work. November 6, 2006. (accessed 24 February 2018).
MLA Format
Henderson, Tom. The Physics Classroom: Definition and Mathematics of Work. 2004. 6 Nov. 2006. 24 Feb. 2018 <>.
BibTeX Export Format
@misc{ Author = "Tom Henderson", Title = {The Physics Classroom: Definition and Mathematics of Work}, Volume = {2018}, Number = {24 February 2018}, Month = {November 6, 2006}, Year = {2004} }
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%A Tom Henderson
%T The Physics Classroom: Definition and Mathematics of Work
%D November 6, 2006
%O text/html

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%0 Electronic Source
%A Henderson, Tom
%D November 6, 2006
%T The Physics Classroom: Definition and Mathematics of Work
%V 2018
%N 24 February 2018
%8 November 6, 2006
%9 text/html

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The Physics Classroom: Definition and Mathematics of Work:

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