Collision Impulse and Momentum Balance
Impulse is the time integral of force and equals momentum change; for a two-body collision, internal impulses are equal and opposite and total momentum is conserved when external impulse is negligible.
Why this shows up in the exam
Contact-force estimates · Molecular pressure on walls · Generic collision setup
Learn the idea
A collision changes each body momentum through equal opposite impulses. During a short hit, large contact forces act briefly; their force-time area changes momentum while external impulses are often negligible.
🧠 Memory hook: Impulse changes momentum; pair impulses cancel for the system.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- J = integral F dt = Delta p — impulse-momentum theorem
- F_avg = Delta p/Delta t — average collision force
- p₁i+p₂i = p₁f+p₂f — two-body momentum balance
How to approach it
- 1Choose axes and the system
- 2Write signed momentum before and after
- 3Use contact time only after finding Delta p
Common slip-ups that cost marks
- •Conserving momentum for one body alone
- •Using peak force as average force
- •Ignoring rebound signs
🌟 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.