1. Physics 101: Lecture 12, Pg 1 Physics 101: Lecture 12 2D Collisions and Center of mass

2. Physics 101: Lecture 12, Pg 2 Example: stopping car V o =40 m/s m = 1500 kg µ s = 0.6 How long does it take the car to stop?

3. Physics 101: Lecture 12, Pg 3 Momentum is Conserved l Momentum is “Conserved” meaning it can not be created nor destroyed è Can be transferred l Total Momentum does not change with time. l This is a BIG deal! 30

4. Physics 101: Lecture 12, Pg 4 Example: collision “before” “after” M 1 =2kg M 2 =3kg M 1 =2kg V o = 5m/s V o = 0m/s Two blocks collide and stick together, what is their final velocity?

5. Physics 101: Lecture 12, Pg 5 Example: collision “before” “after” M 1 =2kg M 2 =3kg M 1 =2kg V o = 5m/s V o = 2m/s Two blocks collide and stick together, What direction is their final velocity? A)Right B)Left C)The final velocity is zero

6. Physics 101: Lecture 12, Pg 6 Example: collision “before” “after” M 1 =2kg M 2 =3kg M 1 =2kg V o = 5m/s V o = 2m/s Two blocks collide and stick together, what is their final velocity?

7. Physics 101: Lecture 12, Pg 7 Example: cannon (explosion) m c = 200kg m b = 5 kg v = 300 m/s What is the velocity of the cannon?

8. Physics 101: Lecture 12, Pg 8

9. Physics 101: Lecture 12, Pg 9 Explosions “before” “after” M m1m1 m2m2 Example: m 1 = M/3 m 2 = 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 = mv 2 /2 = m 2 v 2 /2m = p 2 /2m *  smaller mass has larger KE Is mechanical (kinetic) energy conserved? * NO!! v1v1 v2v2 35 A=1, B=2, C=same 0 = p 1 +p 2 p 1 = -p 2

10. Physics 101: Lecture 12, Pg 10 Collisions or Explosions in Two Dimensions y x before after P total,x and P total,y independently conserved P total,x,before = P total,x,after P total,y,before = P total,y,after 37

11. Physics 101: Lecture 12, Pg 11 before after ppfppf v o = 3m/s F v v cm Example: shooting pool 43 during Mass of both balls is 2kg 30 0 Find final velocity and direction of white ball At rest v v f =2m/s

12. Physics 101: Lecture 12, Pg 12 Example: shooting pool (cont.)

13. Physics 101: Lecture 12, Pg 13 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?

14. Physics 101: Lecture 12, Pg 14 H LL LL m 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? M + m v V V=0 See I.E. 1 in homework Ballistic Pendulum demo 29

15. Physics 101: Lecture 12, Pg 15 Ballistic Pendulum Collision Conserves Momentum After, Conserve Energy Combine:

16. Physics 101: Lecture 12, Pg 16 Center of Mass Center of Mass = Balance point 46 Some objects can’t be balanced on a single point

17. Physics 101: Lecture 12, Pg 17 Example: center of mass m = 0.140 kg 1m 0.1m M = 0.515

18. Physics 101: Lecture 12, Pg 18 Summary Collisions and Explosions Draw “before”, “after” Define system so that F ext = 0 Set up axes Compute P total “before” Compute P total “after” Set them equal to each other Center of Mass (Balance Point) 50