Conservation of Energy

Solving mechanics problems using energy conservation (W_nc = ΔE)

Golden Rule: Total mechanical energy is conserved when no non-conservative forces (friction, air resistance) do work. If friction acts, account for energy lost: W_nc = ΔKE + ΔPE.

• Step 1: Identify initial and final states — Choose a reference height for gravitational PE (usually the lowest point or the final position). Identify what is known at each state: speed, height, spring compression.
• Step 2: Write the energy conservation equation — If no friction: KE₁ + PE₁ = KE₂ + PE₂. If friction acts over distance d: KE₁ + PE₁ − f·d = KE₂ + PE₂. Include spring PE if a spring is compressed or stretched.
• Step 3: Substitute known values and solve — Substitute the known values. Often one of the energies is zero (e.g., starts from rest: KE₁ = 0; or starts at reference height: PE₁ = 0). Solve for the single unknown.