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Conservation of Momentum

Conservation of Momentum. Review of Momentum & Impulse. Multiply velocity by mass to get momentum: p = mv v f = v i + a Δ t becomes ma· Δ t = Δ p or J = F· Δ t = Δ p Conclusion: The net force acting on an object for a period of time changes the object’s momentum.

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Conservation of Momentum

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  1. Conservation of Momentum

  2. Review of Momentum & Impulse • Multiply velocity by mass to get momentum: p = mv • vf = vi + aΔt becomes ma·Δt = Δp or J = F·Δt = Δp • Conclusion: The net force acting on an object for a period of time changes the object’s momentum.

  3. System of Multiple Objects • If no external forces act on the system, the momentum of the system is conserved. • If the objects of a system interact, then the forces involved are action-reaction force pairs. • Since these force pairs are opposite and have the same magnitude, they cancel for the entire system.

  4. Law of Conservation of Momentum • In the absence of any external forces on the system, the momentum of the system will remain constant. → Momentum is conserved. psys, f = psys, i p1f + p2f + … = p1i + p2i + …

  5. Example Two blocks compress a spring with a string holding the blocks together. If the string is then cut, the two blocks will move away from each other. Find the velocity of the 2nd block if the 1st block has a velocity of 2 m/s to the left after separation. (m1 = m2 = 1 kg) pi = pf → 0 = m1v1f + m2v2f → (1)(-2) + (1)v2f → v2f= +2 m/s

  6. Example Find the velocity of m2 in the previous example if m2= 5 kg instead of 1 kg. pi = pf → 0 = m1v1f + m2v2f → (1)(-2) + (5)v2f → v2f = +0.4 m/s

  7. Example A miner (60 kg) who is running at a speed of 4 m/s is chasing a cart of coal (60 kg) that is moving at 2 m/s. What is their combined speed if the miner manages to jump onto the cart? pi = pf → mmvmi + mcvci = mmcfvf → (60)(4)+(60)(2) = (60 + 60)vf → 360 = 120vf → vf = 3 m/s

  8. Learning Goal Know how to apply the law of conservation of momentum. -- No external forces acting on the system.

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