Short on time? This page is the recap. For graphs, energy bar charts and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Every collision of a system with no net external force conserves momentum. The type of collision depends on kinetic energy.
- Elastic: total kinetic energy of the system is the same before and after. One object can lose kinetic energy as long as the other gains the same amount.
- Inelastic: total kinetic energy decreases. Nonconservative forces transform it into internal (thermal) energy, sound and deformation. Total energy is still conserved.
- Perfectly inelastic: the objects stick and move with one velocity. This leaves the least kinetic energy that momentum conservation allows.
- Explosions increase kinetic energy, using stored energy (spring, chemical).
- In this course you will not solve for two unknown final velocities. You may be given one and asked for the other, then asked to classify.
Key relationships
| Relationship | Use it to |
|---|---|
| Σ(mv) before = Σ(mv) after | find an unknown velocity (signed) |
| K_sys = Σ ½mv² | compare kinetic energy before and after (never negative) |
| m₁v₁ + m₂v₂ = (m₁ + m₂)v_f | find the common velocity when objects stick |
| fraction of K transformed = m₂ / (m₁ + m₂) | m₁ moving sticks to m₂ at rest |
| ΔK = K_after − K_before | size of the transformation (negative for inelastic) |
Assumptions behind the numbers
- No net external impulse during the short collision.
- Objects are treated as particles; rotation is ignored.
- “Elastic” is a model. Real collisions are at best close to elastic.
Mistakes to avoid
- Momentum “lost” in a crash. It is kinetic energy that falls.
- Energy conservation across a sticky collision. Use momentum for the collision; use energy only afterwards.
- Judging by individual objects. Classify by the system total.
- Bouncing apart = elastic. Calculate the totals.
- Signs in kinetic energy. Square speeds; K is never negative.
- Early rounding. Keep extra figures until the comparison.
Quick self-check
- A 1.0 kg cart at 4.0 m/s sticks to a 3.0 kg cart at rest. Find the common speed and the kinetic energy before and after. (1.0 m/s; 8.0 J and 2.0 J)
- A moving cart sticks to an identical cart at rest. What fraction of the kinetic energy is transformed? (One half)
- Two balls have 5.0 J of kinetic energy in total before a collision and 5.0 J after, but one ball’s kinetic energy changed. Elastic or inelastic? (Elastic: the system total is unchanged.)
Next: practice questions.