قانون هوك الصيغة (F = kx): مجاني Calculator & الشغلed Examples

Use F = kx for spring force, constant k, or stretch x. cm→m traps, U = ½kx², examples, and a free Hooke's law calculator.

كيفية الاستخدام قانون هوك (Quick Answer)

Hooke's law for an ideal spring is F = kx. The restoring force magnitude is proportional to stretch or compression from the unstretched length.

  • F = k × x — force in newtons.
  • k = F / x — spring constant in N/m.
  • x = F / k — displacement in meters (not total coil length).
  • Elastic energy stored: U = ½ k x² (joules). حوّل cm → m before substituting.

    • Need a checked number now? Open the free Hooke's law calculator (F = kx) — then come back for unit traps and elastic-limit notes.

    What Is F = kx?

    k is stiffness (N/m). x is change in length from equilibrium. Larger k means a stiffer spring: more force for the same stretch.

    Students often search “hooke's law formula” or “F = kx” for this linear spring model. Once two of F, k, and x are known, the third is fixed.

    Rearrangements

  • F = kx.
  • k = F / x.
  • x = F / k.

    • Solve any form on the free Hooke's law calculator.

    Units

  • F → N.
  • k → N/m.
  • x → m (8 cm = 0.080 m).

    • Trap: leaving x as 8 while k is in N/m makes k wrong by 100×.

    Elastic طاقة الوضع

    While F = kx gives force, the work stored in the spring is U = ½kx². Doubling x doubles F but multiplies U by four.

    Full energy walkthrough: elastic potential energy (U = ½kx²).

    الشغلed Examples

    Example 1: F from k = 200 N/m and x = 0.15 m

    F = kx = (200)(0.15) = 30 N.

    Example 2: k from F = 40 N and x = 0.080 m

    k = 40 / 0.080 = 500 N/m.

    Example 3: x from F = 12 N and k = 150 N/m

    x = 12 / 150 = 0.080 m = 8.0 cm. Then U = ½(150)(0.080)² = 0.48 J.

    Check Examples 1–3 on the Hooke's law calculator.

    Elastic Limit

    F = kx only inside the elastic range. Past the elastic limit the spring permanently deforms and force is no longer proportional to x.

    A mass on a spring with F = −kx is SHM with T = 2π√(m/k). Compare: simple harmonic motion calculator.

    أخطاء شائعة

  • Leaving x in centimeters while k is in N/m.
  • Using total spring length instead of stretch from equilibrium.
  • Mixing mass m with spring constant k.
  • Writing spring energy as kx or ½kx instead of ½kx².

    • مجاني قانون هوك Calculator

    Use the free Hooke's law calculator to solve F = kx for force, k, or x with step-by-step working.

    القوة calculator.

    Simple pendulum calculator.

    Master F = kx with clean metres — then verify every spring homework answer.

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