PhysicsMediumClass 11

Potential Energy — Spring PE, gravitational PE

Work, Energy & Power

JEE Qs

Hard

min

Master the relationship between conservative forces, potential energy, and mechanical energy conservation to solve complex problems efficiently.

🧮 Key Formulas

U_g = mgh (gravitational potential energy for uniform gravity field)

U_s = (1/2)kx^2 (spring potential energy, x = displacement from natural length)

F_x = -dU/dx (relation between conservative force and potential energy in 1D)

W_conservative = -ΔU = -(U_final - U_initial) (work done by a conservative force)

1Potential energy is defined only for conservative forces (e.g., gravity, spring force, electrostatic force); it is path-independent.
2The choice of zero potential energy reference point is arbitrary; only the *change* in potential energy (ΔU) has physical significance.
3The force acting on a particle can be derived from its potential energy function using F = -dU/dx (in 1D) or F = -∇U (in 3D).
4For a spring, 'x' in U_s = (1/2)kx^2 represents the displacement from its natural (equilibrium) length, whether stretched or compressed; U_s is always non-negative.
5Equilibrium points occur where F = 0 (i.e., dU/dx = 0). Stable equilibrium (minima of U) has d²U/dx² > 0, while unstable equilibrium (maxima of U) has d²U/dx² < 0.

✕Incorrectly applying potential energy concepts to non-conservative forces like friction or air resistance.
✕Sign errors when relating work done by conservative forces to potential energy (W_c = -ΔU) or when deriving force from potential energy (F = -dU/dx).
✕Confusing the reference point for zero potential energy or applying the spring potential energy formula with an incorrect 'x' value (e.g., using total length instead of displacement from natural length).