2D Collisions

Objectives

Lesson outcomes

Apply conservation of momentum separately in perpendicular directions.
Use vector components or scale diagrams to solve two-dimensional collision problems.
Judge whether kinetic energy is conserved in a collision.

Syllabus

CIE 9702 syllabus points

3 linked

3.3.2 apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between objects in both one and two dimensions (knowledge of the concept of coefficient of restitution is not required)
3.3.3 recall that, for an elastic collision, total kinetic energy is conserved and the relative speed of approach is equal to the relative speed of separation
3.3.4 understand that, while momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place

Lesson Notes

Student guidance and lesson notes

Overview

Two-dimensional collisions use the same conservation principle as one-dimensional collisions, but momentum must be handled as a vector. Treat the perpendicular directions separately.

What You Need to Know

Momentum is conserved for the system in each direction when no external resultant force acts.
Resolve momentum into perpendicular components when objects move at angles.
The total x-momentum before equals the total x-momentum after.
The total y-momentum before equals the total y-momentum after.
Kinetic energy checks tell you whether a collision is elastic or inelastic.

How to Work Through It

Start by drawing a clear before-and-after diagram with directions labelled.
Choose axes that make the components as simple as possible.
Write separate momentum equations for the x- and y-directions.
Use kinetic energy only after the momentum calculation, when the question asks about collision type.

Check Your Understanding

Why can momentum be conserved in two directions at once?
When should you resolve a velocity into components?
How do you decide which direction is positive?
What evidence would show that a collision is inelastic?

Common Mistakes

Adding momentum magnitudes without considering direction.
Mixing x-components and y-components in the same equation.
Assuming kinetic energy is conserved because momentum is conserved.
Losing signs when an object moves left, down, or at an angle greater than 90 degrees.

Next Steps

Practise component diagrams before doing algebra.
Use the revision lesson to connect moments, fluids, Newton’s laws, and momentum into one topic map.