Two-Dimensional Elastic Collisions and Scattering
For an isolated two-dimensional elastic collision, both components of total momentum and total translational kinetic energy are conserved, subject to the collision geometry.
Why this shows up in the exam
Scattering angles · Oblique billiard-ball impacts · Maximum deflection questions
Learn the idea
Momentum is conserved independently in each spatial direction. In a planar collision, one scalar momentum equation is not enough; x and y balances constrain angles while elastic energy supplies another condition.
🧠 Memory hook: Conserve momentum by components, then use elastic energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum p_x,i = sum p_x,f — x-momentum conservation
- sum p_y,i = sum p_y,f — y-momentum conservation
- sum K_i = sum K_f — elastic kinetic-energy condition
How to approach it
- 1Draw all velocity directions
- 2Write x and y momentum balances
- 3Add energy and solve the geometry
Common slip-ups that cost marks
- •Treating vector momentum as one unsigned equation
- •Assuming outgoing paths are always perpendicular
- •Ignoring geometric constraints
🌟 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.