Explicit physics instruction
Momentum p=mv depends linearly on speed, while kinetic energy K=½mv² depends on speed squared. A change can therefore affect the two totals differently.
Always calculate system totals with signed velocities for momentum and squared speeds for kinetic energy.
Use the same defined system and reference frame before and after the collision.
Vocabulary: momentum; kinetic energy; signed velocity; system total; reference frame.
Worked example with reasoning
A 2 kg cart at 4 m/s sticks to an identical stationary cart. Momentum gives final speed 2 m/s. Initial KE=16 J; final KE=8 J, so half the kinetic energy remains.
Guided question
Repeat the calculation for a 1 kg cart at 6 m/s sticking to an identical cart.
Independent work
- Solve three before/after collision energy audits.
- Check momentum independently from kinetic energy.
- Explain one case where momentum is conserved but KE is not.
Misconception check
Do not use signed velocity inside v² to create negative kinetic energy.
Formative understanding check
Why can kinetic energy never be negative in this classical model?
Reveal response
Mass is positive and speed is squared.
Mentor evidence conference
Ask Archaemenes to compare momentum, energy, and impulse representations for consistency.
Teacher guidance
Foundation: Use parallel momentum/energy tables.
Core: Solve and compare both conserved quantities.
Extended: Analyze percent kinetic-energy loss and uncertainty.