Spring force and potential energy of a springकमानी बल और कमानी की स्थितिज ऊर्जा

NCERT Fig 5.7 & 5.8 · interactive diagram

Parts and their functions

• Ideal spring (constant k) (आदर्श कमानी (नियतांक k)) — Massless; obeys Hooke’s law F = −kx. SI unit of k: N m⁻¹.
• Block of mass m (m द्रव्यमान का गुटका) — On a smooth surface; oscillates about x = 0.
• Displacement x (विस्थापन x) — Measured from the relaxed (unstretched) position.
• Restoring force F = −kx (प्रत्यानयन बल F = −kx) — Always towards x = 0. Work done by the spring from 0 to x: W_s = −½kx².
• Potential energy V = ½kx² (स्थितिज ऊर्जा V = ½kx²) — A parabola; same for stretch and compression. The spring force is conservative.
• Total energy E (कुल ऊर्जा E) — E = K + V = ½kxₘ² = ½mvₘ², constant (no friction).
• Turning points ±xₘ (वापसी बिंदु ±xₘ) — Here V = E and K = 0. Example 5.8: xₘ = √(2K/k) = √(2 × 1.25 × 10⁴ / 5.25 × 10³) = 2.18 m.
• Kinetic energy at x = 0 (x = 0 पर गतिज ऊर्जा) — All energy is kinetic at the centre: speed is maximum vₘ.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 5.7 & 5.8. Report a mistake