Collisions and Explosions: Momentum Conservation
Year 11 Physics Understanding momentum in complex interactions Building on momentum fundamentals
Learning Objectives
Calculate momentum in collisions where objects separate Understand momentum conservation in explosions Apply conservation laws to real-world scenarios Practice exam-style momentum problems
Quick Recap: What You Already Know
Momentum = mass × velocity (p = mv) Momentum is conserved in collisions When objects stick together: m₁v₁ + m₂v₂ = (m₁ + m₂)vfinal Units: kg⋅m/s or N⋅s
Think About This...
What happens to momentum when two objects collide and bounce apart? Is momentum still conserved? How do we calculate the final velocities?
Collisions Where Objects Don't Stick
Called 'elastic collisions' Objects separate after impact Total momentum is STILL conserved Kinetic energy may also be conserved
Elastic vs Inelastic Collisions
{"left":"Objects bounce apart\nKinetic energy conserved\nExample: billiard balls","right":"Objects stick together\nKinetic energy lost to heat/sound\nExample: car crash"}
The Conservation Equation
Before collision: m₁v₁ + m₂v₂ After collision: m₁v₁' + m₂v₂' Conservation: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' Note: v₁' and v₂' are the final velocities
Worked Example 1
Ball A (2 kg) moving at 3 m/s hits stationary Ball B (1 kg) After collision: Ball A moves at 1 m/s Find the velocity of Ball B after collision Use: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Solution to Example 1
Initial momentum: (2 kg)(3 m/s) + (1 kg)(0 m/s) = 6 kg⋅m/s Final momentum: (2 kg)(1 m/s) + (1 kg)(v₂') = 2 + v₂' Conservation: 6 = 2 + v₂' Therefore: v₂' = 4 m/s
Understanding Explosions
Objects start at rest or moving together Internal forces cause separation Total momentum before = Total momentum after Example: firework exploding in air
Explosion Characteristics
{"left":"Objects start together\nInternal energy creates separation\nMomentum conserved throughout","right":"Light objects move faster\nHeavy objects move slower\nTotal momentum unchanged"}
Worked Example 2: Explosion
A 6 kg object at rest explodes into two pieces Piece A: 2 kg moving at 9 m/s to the right Find the velocity of Piece B (4 kg) Initial momentum = 0 (object at rest)
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