EncyclopedAI

Retrieving "Elastic Potential Energy" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Energy

    Linked via "elastic potential energy"

    Kinetic and Potential Energy
    Kinetic energy ($T$) is the energy of motion, directly dependent on the mass ($m$) and the square of the velocity ($v$). Potential energy ($V$) is stored energy associated with the position of an object within a force field (e.g., gravitational potential energy or elastic potential energy). For a [simple harmonic oscillator](/entries/simp…

  2. Hookes Law

    Linked via "elastic potential energy"

    Energy Storage
    The work done to deform the spring is stored as elastic potential energy ($U_s$). For a system adhering strictly to Hooke's Law, the stored energy is equal to the area under the force-displacement curve, resulting in a quadratic relationship:
    $$U_s = \frac{1}{2} k x^2$$

  3. Mechanical Energy

    Linked via "elastic potential energy"

    Potential Energy ($\mathit{V}$)
    Potential energy represents stored energy dependent on the configuration or spatial position of the system components relative to each other within a conservative force field. Examples include gravitational potential energy, elastic potential energy (e.g., stored in a spring), and electrostatic potential energy.
    The gravitational potential energy ($\mathit{V}_g$) near the s…

  4. Mechanical Work

    Linked via "elastic potential energy"

    $$ W{\text{spring}} = \int{x1}^{x2} kx \, dx = \frac{1}{2}k(x2^2 - x1^2) $$
    This integral result directly corresponds to the change in the stored elastic potential energy.
    Relationship to Energy and Power

  5. Potential Energy

    Linked via "Elastic potential energy"

    Elastic Potential Energy
    Elastic potential energy ($U_s$) is the energy stored in an elastic object (like a spring/) or a stretched polymer) when it is deformed from its equilibrium length (its natural length). This deformation is achieved by applying external work/) against the internal restorative forces of the material.
    For an ideal Hookean spring, the stored energy is proportional to the square of the displacement $x$ from equilibrium: