Conservation Conditions
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Before you conserve something, check its condition. Momentum is conserved when there’s no net external force. Mechanical energy is conserved when no outside forces do net work and no energy is turned into internal energy (no friction, no sticking, no air resistance). One can hold without the other.
1. Two different checklists
2. Check each situation
3. Example, then try it
Two carts on a frictionless track are pushed apart by a compressed spring between them. What is conserved?
Momentum: the spring’s forces are internal, and the track is frictionless. ✓
Mechanical energy: the spring’s stored energy becomes kinetic energy, with nothing lost to heat. K + Us stays the same. ✓
A 0.020 kg bullet moving at 300 m/s embeds in a 1.98 kg block hanging on a string, and the block swings up. How high does it rise? (g = 10 m/s²)
Collision (sticks): momentum ✓, mechanical energy ✗. So use momentum: (0.020)(300) = (2.0)v → v = 3.0 m/s.
Swing: now the string’s tension does no work and nothing sticks, so mechanical energy ✓ (momentum ✗).
Energy: ½(2.0)(3.0)² = (2.0)(10)h → 9.0 = 20h → h = 0.45 m.
Why it matters: using energy for the collision too would give h = 45 m, a hundred times too high.
Answer: 0.45 m. Use momentum for the collision and energy for the swing.
4. Common mistakes
A box slides across a rough floor and comes to a stop. For the box alone, which quantity is conserved?
Friction is an external force on the box, so its momentum changes. Friction also turns its kinetic energy into internal energy, so mechanical energy isn’t conserved either.
Ready to practice?
4 questions on Conservation Conditions, each with a hint and an explanation for every wrong answer.