Elastic Energi potensial Rumus (U = ½kx²): Calculator & Examples

Hitung spring energy with U = ½kx². Link to F = kx, unit traps (cm vs m), worked examples, and free Hooke's law and PE calculators.

What Elastic Energi potensial Asks

Elastic potential energy is the energy stored in a stretched or compressed spring. Intro physics writes it as U = ½ k x² (also written PEₛ = ½kx² or Us = ½kx²).

k is the spring constant in N/m. x is the displacement from the unstretched length in meters — not the full coil length. Energi comes out in joules.

Hooke's law F = kx gives the force; elastic PE stores the work done while stretching. Check force problems on the free Hooke's law calculator, then use U = ½kx² for energy.

The Rumus

  • U = ½ k x² — elastic potential energy in joules.
  • If you know U and k: |x| = √(2U / k).
  • If you know U and x: k = 2U / x².

    • Because x is squared, stretch and compression store the same energy for the same |x|. Doubling the stretch multiplies stored energy by four.

    How U Connects to F = kx

    The spring force grows linearly with x. The work to stretch from 0 to x is the area under the F-vs-x line: a triangle with area ½ × base × height = ½ × x × (kx) = ½kx². That work becomes elastic potential energy in an ideal spring.

    For gravitational PE = mgh instead of spring energy, see how to calculate potential energy (mgh).

    Units

  • k → N/m.
  • x → m (convert cm first: divide by 100).
  • U → J (1 J = 1 N·m).

    • Usahaed Examples

    Example 1: find U

    k = 200 N/m, x = 0.15 m. U = ½(200)(0.15)² = 100 × 0.0225 = 2.25 J.

    Example 2: leave x in cm by mistake

    Same spring, x written as 15 instead of 0.15. Fake U = ½(200)(15)² = 22,500 J — wrong by a factor of 10,000. Always convert centimeters to meters.

    Example 3: find stretch from energy

    U = 0.80 J, k = 160 N/m. x² = 2U/k = 1.6/160 = 0.010. |x| = 0.10 m = 10 cm.

    Example 4: compare to Hooke force

    k = 200 N/m, x = 0.15 m. Gaya magnitude F = kx = 30 N, but energy U = 2.25 J. Do not treat F and U as interchangeable.

    When the Rumus Fails

  • Past the elastic limit (permanent deformation) — F ≠ kx and U ≠ ½kx².
  • Non-ideal springs with friction or plasticity inside the coil.
  • Using gravitational mgh when the problem is about a spring, or the reverse.

    • Kesalahan umum

  • Writing U = kx or U = ½kx instead of ½kx².
  • Leaving x in centimeters while k is in N/m.
  • Using total spring length instead of stretch from equilibrium.
  • Confusing elastic PE with kinetic energy ½mv² or gravitational mgh.

    • Check Related Tools

    Hooke's law calculator — F = kx for force, k, or x.

    Potential energy calculator — gravitational PE = mgh.

    Kinetic energy calculator — KE = ½mv².

    SHM calculator — mass-spring period T = 2π√(m/k).

    Learn U = ½kx² and keep force problems on F = kx.

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