Dynamics II: Momentum

Momentum & Energy

discussion summary practice problems Momentum & Energy Discussion general info two objects (1 and 2), velocities before and after (unprime and prime) conservation of momentum m1v1 + m2v2 = m1v′1 + m2v′2 “conservation of kinetic energy” — not a law, just a statement of a possibility ½m1v12 + ½m2v22 = ½m1v′12 + ½m2v′22 Solve for the velocities after collision. (This is a painful process.) There are two pairs of solutions. v′1 =  (m1 − m2)v1  + 2m2v2 ...

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Conservation Of Momentum

discussion summary practice problems Conservation Of Momentum Discussion start Start with Newton’s third law of motion, toss in the impulse-momentum theorem, and see what happens. +F1 = −F2 +F1Δt = −F2Δt +m1Δv1 = −m2Δv2 +Δp1 = −Δp2 +(p1′ − p1) = −(p2′ − p2) p1′ + p2′ = p1 + p2 ∑p′ = ∑p Or flip it around. ∑p = ∑p′ The total momentum before an interaction is the same as the total momentum after the interaction. ...

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Impulse & Momentum

discussion summary practice problems Impulse & Momentum Discussion what is impulse ? Momentum keeps me going. From the Principia. Quantitas motus est mensura ejusdem orta ex velocitate et quantite materiæ conjunctim.   The quantity of motion is the measure of the same, arising from the velocity and the quantity of matter conjunctly. We now call this quantity momentum. Momentum is resistance to stopping. ...

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