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Physics 101: Lecture 12 2D Collisions and Center of mass

Physics 101: Lecture 12 2D Collisions and Center of mass. Example: stopping car. m = 1500 kg. How long does it take the car to stop?. V o =40 m/s. µ s = 0.6. Momentum is Conserved. Momentum is “Conserved” meaning it can not be created nor destroyed Can be transferred

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Physics 101: Lecture 12 2D Collisions and Center of mass

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  1. Physics 101: Lecture 122DCollisions and Center of mass

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

  3. 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

  4. 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?

  5. 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 direction is their final velocity? • Right • Left • The final velocity is zero

  6. 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?

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

  8. “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

  9. y x before after Collisions or Explosions in Two Dimensions • Ptotal,xand Ptotal,yindependently conserved • Ptotal,x,before = Ptotal,x,after • Ptotal,y,before = Ptotal,y,after 37

  10. vo = 3m/s F vf =2m/s Example: shooting pool during after before pf vcm 300 At rest Mass of both balls is 2kg vf =2m/s Find final velocity and direction of white ball 43

  11. Example: shooting pool (cont.)

  12. Block 1 of mass M1 = 10kg has an initial velocity of 5m/s in the +x direction. It collides with Block 2 of mass M2 = 5kg which, initially has a velocity of 15m/s in the +y direction. If the two blocks stick together what is the final speed and direction of the two blocks?

  13. Ballistic Pendulum L L V=0 L L m H v M + m V M A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L. Subsequently, m+M rise to a height of H. Given H, M and m what is the initial speed v of the projectile? demo See I.E. 1 in homework 29

  14. Ballistic Pendulum Collision Conserves Momentum After, Conserve Energy Combine:

  15. Center of Mass = Balance point Center of Mass Some objects can’t be balanced on a single point 46

  16. Example: center of mass 1m m = 0.140 kg 0.1m M = 0.515

  17. Summary • 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 • Center of Mass (Balance Point) 50

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