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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 3: Work, Energy & PowerTranslational Kinetic Energy & Potential EnergyElastic Potential Energy

Elastic Potential Energy (College Board AP® Physics 1: Algebra-Based)

Study Guide

Leander Oates

Written by: Leander Oates

Reviewed by: Caroline Carroll

Elastic potential energy

  • The potential energy of common physical systems can be described using the physical properties of that system

  • Elastic potential energy is defined as:

The energy stored within a material (e.g. a spring) when it is stretched or compressed

  • Therefore, for a material obeying Hooke’s Law, the elastic potential energy of an ideal spring can be calculated using:

U subscript s space equals space 1 half k open parentheses increment x close parentheses squared

  • Where:

    • U subscript s = elastic potential energy, measured in straight J

    • k = spring constant, measured in straight N divided by straight m

    • increment x = distance the spring has been stretched or compressed from it's equilibrium length, measured in straight m

  • Elastic potential energy is a scalar quantity with magnitude only

Diagram of three springs with attached masses, showing unstretched, stretched, and compressed states, with energy equations and displacement denoted as Δx.
A spring that is stretched or compressed has elastic potential energy

  • It is very dangerous if a wire under large stress suddenly breaks because the elastic potential energy of the strained wire is converted into kinetic energy

elastic space potential space energy space equals space kinetic space energy

U subscript s space equals space K 

1 half k open parentheses increment x close parentheses squared space equals space 1 half m v squared

v space proportional to space increment x

  • This equation shows

    • The greater the extension of a wire increment x the greater the speed v it will have when it breaks

Worked Example

Cars are built with shock absorbers to make a ride more comfortable. Shock absorbers are strong springs that absorb energy when the car goes over a bump.

A shock absorber spring has a spring constant of 52 space kN divided by straight m is fixed next to a wheel and compressed a distance of 10 space cm. Which of the following is the correct value for the elastic potential energy of the spring?

A: 26 space straight N times straight m

B: 260 space straight N times straight m

C: 2600 space straight N times straight m

D: 26 space 000 space straight N times straight m

The correct answer is B

Step 1: List the known values

  • Spring constant, k space equals space 52 space kN divided by straight m space equals space 52 cross times 10 cubed space straight N divided by straight m

  • Compression,increment x space equals space 10 space cm space equals space 10 cross times 10 to the power of negative 2 end exponent space straight m 

Step 2: Substitute the values into the elastic potential energy equation

U subscript s space equals space 1 half k open parentheses increment x close parentheses squared

U subscript s space equals space 1 half open parentheses 52 cross times 10 cubed close parentheses open parentheses 10 cross times 10 to the power of negative 2 end exponent close parentheses squared

U subscript s space equals space 260 space straight N times straight m

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    Author
    Reviewer
    Leander Oates

    Author: Leander Oates

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.