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Physics 101: Lecture 11 Momentum and Impulse

This lecture covers the concepts of momentum and impulse in physics, including the definitions, calculations, and conservation principles. Examples and demonstrations are used to illustrate these ideas.

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Physics 101: Lecture 11 Momentum and Impulse

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  1. Physics 101: Lecture 11Momentum and Impulse

  2. Key Ideas • Last Time: Work-Energy • S F = m a multiply both sides by d • S F d= m a d (note a d = ½ Dv2) • S F d= ½ m Dv2 • S W = DKE Define Work and Kinetic Energy • This Time: Impulse-Momentum • S F = m a multiply both sides by Dt • S F Dt= m a Dt (note a Dt = Dv) • S F Dt= m Dv • S I = Dp Define Impulse and Momentum 08

  3. Demo/Example Two identical balls are dropped from the same height onto the floor. In each case they have velocity v downward just before hitting the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the magnitude of the impulse given to the ball by the floor the biggest? A. Case 1 B. Case 2 C. The same Bouncing Ball Sticky Ball 16

  4. time Question In both cases of the above question, the direction of the impulse given to the ball by the floor is the same. What is this direction? A. Upward B. Downward 19

  5. Demo You throw an egg into 1) A sheet 2) A wall In both cases, the egg stops. In which case is the impulse greater? A) Sheet B) Wall C) the same I = DP Same change in momentum In which case is the average force greater A) Sheet B) Wall C) the same Dp = F Dt F = Dp/Dt Smaller Dt = large F 24

  6. Example: stopping car m = 1500 kg How long does it take the car to stop? Vo=40 m/s µs = 0.6

  7. Momentum is Conserved • Momentum is “Conserved” meaning it can not be created nor destroyed • Can be transferred • Total Momentum does not change with time. • This is a BIG deal! 30

  8. M2=3kg M2=3kg M1=2kg M1=2kg Example: collision “after” “before” Vo = 0m/s Vo = 5m/s Two blocks collide and stick together, what is their final velocity?

  9. M2=3kg M2=3kg M1=2kg M1=2kg Example: collision “after” “before” Vo = 2m/s Vo = 5m/s Two blocks collide and stick together, what is their final velocity?

  10. Example: cannon (explosion) mc = 200kg What is the velocity of the cannon? mb = 5 kg v= 300 m/s

  11. “before” M “after” m2 m1 Explosions A=1, B=2, C=same v1 v2 • Example: m1 = M/3 m2 = 2M/3 • Which block has larger |momentum|? • Each has same |momentum| • Which block has larger speed? • mv same for each  smaller mass has larger velocity • Which block has larger kinetic energy? • KE = mv2/2 = m2v2/2m = p2/2m •  smaller mass has larger KE • Is mechanical (kinetic) energy conserved? • NO!! 0 = p1+p2 p1= -p2 35

  12. Collisions and Explosions Draw “before”, “after” Define system so that Fext = 0 Set up axes Compute Ptotal “before” Compute Ptotal “after” Set them equal to each other Impulse and Momentum Summary 33

  13. Summary • Impulse I = FDt • Gives change in momentum I = Dp • Momentum p = mv • Momentum is VECTOR • Momentum is conserved (when SF = 0) • S mvinitial = S mvfinal 50

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