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This interactive homework problem was designed to help students understand how to apply calculations in a system involving a mass hanging from a vertical spring. If the spring is stretched and then released, what is the speed of the block when it returns to its original position for the first time? First, learners will answer conceptual questions designed to encourage critical thinking, then they will use the Conservation of Mechanical Energy method to solve the problem. This resource is part of a larger collection of interactive problems developed by the Illinois Physics Education Research Group.
Editor's Note: We recommend this resource to promote deep understanding of the factors that influence the motion of a mass hanging from a spring. The author anticipates student conceptual roadblocks and helps them recognize how to use alternative problem-solving methods when the kinematic equations would become overly tedious. Meets numerous Math Common Core standards and AAAS Benchmarks.
Subjects Levels Resource Types
Classical Mechanics
- Work and Energy
= Conservation of Energy
Education Practices
- Active Learning
= Problem Solving
Oscillations & Waves
- Oscillations
= Springs and Oscillators
- High School
- Instructional Material
= Activity
= Problem/Problem Set
= Tutorial
Appropriate Courses Categories Ratings
- Conceptual Physics
- Algebra-based Physics
- AP Physics
- Activity
- Assessment
- New teachers
• Currently 0.0/5

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Intended User:
Learner
Format:
text/html
Access Rights:
Free access
Restriction:
© 2006 University of Illinois Physics Education Research Group
Keywords:
Socratic reasoning, conservation of mechanical energy, conservative forces, elastic energy, gravitational potential energy, kinetic energy, potential energy, spring, tutorial problem
Record Cloner:
Metadata instance created February 9, 2008 by Alea Smith
Record Updated:
January 29, 2015 by Caroline Hall
Last Update
when Cataloged:
June 16, 2006

### 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/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.
4F. Motion
• 6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
• 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

#### 11. Common Themes

11A. Systems
• 9-12: 11A/H1. A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts.

#### 12. Habits of Mind

12B. Computation and Estimation
• 9-12: 12B/H1. Use appropriate ratios and proportions, including constant rates, when needed to make calculations for solving real-world problems.
• 9-12: 12B/H2. Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable.

### Common Core State Standards for Mathematics Alignments

#### High School — Number and Quantity (9-12)

Quantities? (9-12)
• N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

#### High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)
• A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
• A-SSE.2 Use the structure of an expression to identify ways to rewrite it.
Creating Equations? (9-12)
• A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

This resource is part of a Physics Front Topical Unit.

Topic: Periodic and Simple Harmonic Motion
Unit Title: Conservation of Energy and Forces on a Spring

We highly recommend this resource to promote deeper understanding of the interactions that influence the motion of a mass hanging from a spring. The author anticipates student conceptual roadblocks and helps them recognize how to use alternative problem-solving methods when the kinematic equations would become overly tedious. Meets numerous Math Common Core standards and AAAS Benchmarks and would be a good supplement for the PhET simulation "Masses & Springs" (above under Activities).

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AIP Format
G. Gladding, (University of llinois Physics Education Research Group, Urbana, 2006), WWW Document, (https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring).
AJP/PRST-PER
G. Gladding, Illinois PER Interactive Examples: Mass on a Vertical Spring (University of llinois Physics Education Research Group, Urbana, 2006), <https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring>.
APA Format
Gladding, G. (2006, June 16). Illinois PER Interactive Examples: Mass on a Vertical Spring. Retrieved September 11, 2024, from University of llinois Physics Education Research Group: https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring
Chicago Format
Gladding, Gary. Illinois PER Interactive Examples: Mass on a Vertical Spring. Urbana: University of llinois Physics Education Research Group, June 16, 2006. https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring (accessed 11 September 2024).
MLA Format
Gladding, Gary. Illinois PER Interactive Examples: Mass on a Vertical Spring. Urbana: University of llinois Physics Education Research Group, 2006. 16 June 2006. 11 Sep. 2024 <https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring>.
BibTeX Export Format
@misc{ Author = "Gary Gladding", Title = {Illinois PER Interactive Examples: Mass on a Vertical Spring}, Publisher = {University of llinois Physics Education Research Group}, Volume = {2024}, Number = {11 September 2024}, Month = {June 16, 2006}, Year = {2006} }
Refer Export Format

%A Gary Gladding %T Illinois PER Interactive Examples: Mass on a Vertical Spring %D June 16, 2006 %I University of llinois Physics Education Research Group %C Urbana %U https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring %O text/html

EndNote Export Format

%0 Electronic Source %A Gladding, Gary %D June 16, 2006 %T Illinois PER Interactive Examples: Mass on a Vertical Spring %I University of llinois Physics Education Research Group %V 2024 %N 11 September 2024 %8 June 16, 2006 %9 text/html %U https://per.physics.illinois.edu/per/IE/ie.pl?phys111/ie/06/IE_mass_vertical_spring

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### Illinois PER Interactive Examples: Mass on a Vertical Spring:

Is Part Of Illinois PER: Interactive Examples

The full collection of interactive homework problems developed by author Gary Gladding.

relation by Caroline Hall
Same topic as PhET Teacher Activities: Hooke's Law

A lesson on Hooke's Law, developed specifically to accompany the PhET simulation Masses & Springs

relation by Caroline Hall

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