Inelastic Collisions and Energy Loss
In a perfectly inelastic collision the bodies coalesce and momentum is conserved when external impulse is negligible, while kinetic-energy loss is the positive difference K_i-K_f.
Why this shows up in the exam
Bullets embedding in blocks · Bodies that coalesce · Successive sticking collisions
Learn the idea
Momentum may be conserved while kinetic energy decreases. Sticking bodies share a final velocity, and missing kinetic energy becomes deformation, heat, sound, or internal energy.
🧠 Memory hook: Stick first with momentum; count energy loss afterward.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m1u1+m2u2 = (m1+m2)V — one-dimensional sticking collision
- Delta K_loss = K_i-K_f — kinetic energy converted internally
- K_loss = (1/2)mu(u1-u2)² — two-body perfectly inelastic loss
How to approach it
- 1Conserve vector momentum through impact
- 2Find the shared final velocity
- 3Compute kinetic-energy loss separately
Common slip-ups that cost marks
- •Conserving kinetic energy while bodies stick
- •Applying energy conservation across deformation
- •Using center-of-mass speed for one body
🌟 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
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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.