Elastic Collisions in One Dimension
A collision in which both momentum and kinetic energy are conserved; for equal masses the bodies exchange velocities.
What is Elastic Collisions in One Dimension?
A collision where there is no net loss in kinetic energy in the system as a result of the collision.
Key formula / rule: Final Velocity of Mass 1 (v1)
Key points
- Apply conservation laws to solve for post-collision velocities.
- Understand the physical significance of the Coefficient of Restitution.
- Analyze special cases involving varying mass ratios.
Common exam trap
Confusing elastic collisions with inelastic ones where KE is not conserved.
Definitions
- Term
Elastic Collision
- Meaning
A collision where there is no net loss in kinetic energy in the system as a result of the collision.
- Term
Velocity of Separation
- Meaning
The relative velocity at which two objects move away from each other after a collision.
Learning objectives
Apply conservation laws to solve for post-collision velocities.
Understand the physical significance of the Coefficient of Restitution.
Analyze special cases involving varying mass ratios.
Formulae
- Name
Final Velocity of Mass 1 (v1)
- Note
Standard 1D elastic collision formula.
- Expression
v1 = [(m1 - m2) / (m1 + m2)] * u1 + [2 * m2 / (m1 + m2)] * u2
- Name
Final Velocity of Mass 2 (v2)
- Note
Symmetric to the formula for v1.
- Expression
v2 = [(m2 - m1) / (m1 + m2)] * u2 + [2 * m1 / (m1 + m2)] * u1
- Name
Coefficient of Restitution (e)
- Note
For perfectly elastic collisions, e = 1.
- Expression
e = (v2 - v1) / (u1 - u2)
Prerequisites
Newton's Laws of Motion
Work-Energy Theorem
Linear Momentum
Common mistakes
Confusing elastic collisions with inelastic ones where KE is not conserved.
Signs: Forgetting that velocity is a vector; always define a positive direction.
Assuming KE is conserved during the impact (deformation phase) rather than just before and after.
Keywords
Momentum
Kinetic Energy
Elastic
Velocity Exchange
Coefficient of Restitution
Practice preview
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