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PhysicsMediumClass 11
Conservative vs Non-Conservative Forces
Work, Energy & Power
7
JEE Qs
8%
Hard
50
min
Master the definitions and implications of conservative/non-conservative forces for energy conservation and understand their mathematical tests for problem-solving.
🧮 Key Formulas
W_conservative = -ΔU = U_initial - U_final
W_non-conservative = ΔE_mech = ΔK + ΔU
F_x = -dU/dx (for a 1D conservative force)
F = -∇U (for a 3D conservative force, where ∇ is the gradient operator)
∇ x F = 0 (Curl of a conservative force is zero for 3D, indicating irrotationality)
E_mech = K + U (Total mechanical energy)
✅ Key Points for JEE
- 1Work done by a conservative force depends only on the initial and final positions, not on the path taken. Work done by a conservative force in any closed loop is zero.
- 2Conservative forces are associated with potential energy (U). If only conservative forces do work on a system, its total mechanical energy (K + U) remains conserved.
- 3Work done by a non-conservative force is path-dependent. These forces generally dissipate (e.g., friction, air resistance) or add (e.g., external applied force) energy to the system, causing a change in its total mechanical energy (W_NC = ΔK + ΔU = ΔE_mech).
- 4To mathematically test if a force F is conservative: (a) For 1D, if F_x can be expressed as -dU/dx for some potential energy function U. (b) For 2D/3D, if its curl (∇ x F) is zero, or if the work done by it between any two points is path independent.
- 5Common examples: Gravity and ideal spring force are conservative. Friction, air resistance, viscous drag, and most applied forces are non-conservative.
⚠️ Common Mistakes
- ✕Incorrectly assuming mechanical energy is always conserved, even when non-conservative forces are acting, failing to apply W_NC = ΔE_mech.
- ✕Confusing the work done by *all* forces (W_net = ΔK) with the work done by *non-conservative* forces (W_NC = ΔE_mech).
- ✕Attributing a potential energy function to non-conservative forces, which is fundamentally incorrect.
- ✕Not knowing how to apply the mathematical tests (F = -∇U or ∇ x F = 0) to determine if a given force field is conservative, especially in vector form.
NCERT Chapters
- Class 11 Physics Ch 6: Work, Energy and Power