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Lecture 11: Momentum and Impulse

Lecture 11: Momentum and Impulse. Conservation of Momentum Impulse & Momentum. Conservation of Momentum. Momentum is “Conserved” meaning it cannot be created nor destroyed! Momentum can be transferred. Total Momentum does not change with time. This is a BIG deal!. Momentum & Impulse.

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Lecture 11: Momentum and Impulse

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  1. Lecture 11:Momentum and Impulse • Conservation of Momentum • Impulse & Momentum

  2. Conservation of Momentum • Momentum is “Conserved” meaning it cannot be created nor destroyed! • Momentum can be transferred. • Total Momentum does not change with time. • This is a BIG deal!

  3. Momentum & Impulse • Review of work and kinetic energy: • Now, define impulse and momentum:

  4. Pushing Off… • An astronaut (with mass 60 kg) in outer space pushes of her spacecraft (with mass 400 kg) with a force F = 500 N for 0.3 s. • The impulse on the astronaut is: • I = Ft = (500 N)*(0.3 s) = 150 N-s • The final speed of the astronaut is: • p = 150 N-s … vf = 2.5 m/s

  5. Pushing Off…(continued) • An astronaut (with mass 60 kg) in outer space pushes of her spacecraft (with mass 400 kg) with a force F = 500 N for 0.3 s. • The impulse on the spacecraft is equal and opposite (by Newton’s Third Law): • I = Ft = (-500 N)*(0.3 s) = -150 N-s • The final speed of the spacecraft is: • p = -150 N-s … vf = -0.375 m/s

  6. Summary • Momentum p = mv • Momentum is a VECTOR • Momentum is conserved (when SF = 0) • S mvinitial = S mvfinal • Impulse I = FDt • Gives change in momentum I = Dp

  7. Momentum Example • At an amusement park, two bumper cars have a head-on collision. The first car has a total mass of 300 kg and is initially moving to the right at 4 m/s. The second car has a mass of 250 kg and is initially moving to the left at 4 m/s. The first car rebounds back to the left at 1 m/s. What is the final velocity of the second car? • We will use conservation of momentum! • (The net external force on the system is zero.)  mvinitial =  mvfinal

  8. Momentum Example • At an amusement park, two bumper cars have a head-on collision. The first car has a total mass of 300 kg and is initially moving to the right at 4 m/s. The second car has a mass of 250 kg and is initially moving to the left at 4 m/s. The first car rebounds back to the left at 1 m/s. What is the final velocity of the second car? • p = mv • define positive to the right • there are two cars on each side of the momentum equation m1v1i + m2v2i = m1v1f + m2v2f (300 kg)(4 m/s) + (250 kg)(-4 m/s) = (300 kg)(-1 m/s) + (250 kg)(v2f)

  9. Momentum Example • At an amusement park, two bumper cars have a head-on collision. The first car has a total mass of 300 kg and is initially moving to the right at 4 m/s. The second car has a mass of 250 kg and is initially moving to the left at 4 m/s. The first car rebounds back to the left at 1 m/s. What is the final velocity of the second car? • car 2 rebounds back to the right V2f = +2 m/s

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