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MathidiaMathematics Academy
Further mechanics
Lesson 60 of 75
Review

Further mechanics modelling

Objective. Combine momentum, energy and force in unfamiliar systems.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Further mechanics modelling combines several mechanical principles—momentum, energy, circular motion or forces—into a single multi-stage problem, requiring a clear identification of which principle applies at each stage of the motion. A typical approach sets up the scenario with a diagram, lists known and unknown quantities, chooses the correct conservation law or equation of motion for each phase, and checks that units and signs are consistent throughout. For example, a particle might be projected, undergo circular motion on a track, then experience a collision, each phase needing a different physical law.

Worked example

A particle of mass 3kg slides down a smooth slope from rest, descending a vertical height of 2m, before colliding with a stationary particle of mass 1kg, coalescing with it. Using energy and momentum modelling, find the speed of the combined particle immediately after the collision.

321
Bar chart of the values 3, 2, 1
  1. 1Use energy conservation on the slope: ½mv² = mgh, so v² = 2gh = 2(9.8)(2) = 39.2, giving v ≈ 6.26 m/s
  2. 2Since the particles coalesce, momentum is conserved: m₁v = (m₁+m₂)v'
  3. 3Substitute: 3(6.26) = 4v', so v' = 18.78/4
  4. 4v' ≈ 4.69 m/s

Answer: v' ≈ 4.69 m/s

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Common mistake. Students apply a single formula to the whole problem without recognising it changes into distinct physical phases, each needing a different principle (e.g. using suvat equations through a collision where momentum conservation is actually required). Always identify phase boundaries in the motion before choosing which law applies.

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