훅의 법칙 공식 (F = kx): 무료 계산기 & 풀이 예제

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

사용 방법 훅의 법칙 (Quick 답)

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

  • F = k × x — 힘 in newtons.
  • k = F / x — spring constant in N/m.
  • x = F / k — 변위 in meters (not total coil length).
  • 탄성 에너지 stored: U = ½ k x² (joules). 변환 cm → m before substituting.

    • Need a 확인ed 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 힘 for the same stretch.

    학생 often search “hooke's law 공식” 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.

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

    단위

  • 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×.

    탄성 위치 에너지

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

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

    풀이 예제

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

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

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

    k = 40 / 0.080 = 500 N/m.

    예제 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.

    확인 예제 1–3 on the Hooke's law calculator.

    탄성 Limit

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

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

    흔한 실수

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

    • 무료 훅의 법칙 계산기

    Use the free Hooke's law calculator to solve F = kx for 힘, k, or x with 단계별 일ing.

    힘 calculator.

    Simple pendulum calculator.

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

    문서

    • 탄성 위치 에너지 공식 (U = ½kx²): 계산기 & 예제
    • 계산 방법 전기 전력 (P = VI, I²R, V²/R)
    • 계산 방법 파동 속도 (v = fλ): 주파수 × 파장
    • 계산 방법 무게 (W = mg): 질량 vs 힘
    • 계산 방법 밀도 (ρ = m/V): 질량 ÷ Volume
    • 계산 방법 가속도 (a = (v − u)/t)

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