One-Dimensional Elastic Collisions
A perfectly elastic head-on collision is determined by conservation of linear momentum together with relative speed of separation equal to relative speed of approach.
Why this shows up in the exam
Head-on mass collisions · Maximum energy transfer · Collision chains
Learn the idea
A one-dimensional elastic collision conserves momentum and kinetic energy. For equal masses, velocities exchange; for unequal masses, mass contrast controls reversal, transfer, and energy sharing.
🧠 Memory hook: Momentum plus relative speed solves elastic head-on impacts.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m1u1+m2u2 = m1v1+m2v2 — momentum conservation
- u1-u2 = -(v1-v2) — elastic relative-speed rule
- v1 = ((m1-m2)u1+2m2u2)/(m1+m2) — first-body final velocity
How to approach it
- 1Choose one positive direction
- 2Write momentum conservation
- 3Apply e=1 and test limiting cases
Common slip-ups that cost marks
- •Conserving each body kinetic energy
- •Using equal-mass exchange for unequal masses
- •Losing signs when a body rebounds
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.