1. 2D Collisions and Center of mass1

2. Collisions or Explosions in Two Dimensionsy x
after
before
Ptotal,x and Ptotal,y independently conserved
Ptotal,x,before = Ptotal,x,after
Ptotal,y,before = Ptotal,y,after 37

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

4. Example: shooting pool (cont.)

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

6. Example: center of mass
m = kg
0.1m
M =
0.515

7. Velocity of Center of Mass
The speed of the balance point 46

8. Elastic Collisions Find Vcm.
Subtract Vcm from both initial velocities.
Change sign of both velocities.
Add Vcm to both velocities.

9. Example: collision “before” “after”
Vo = 3m/s
Vo = 0m/s
M1=2kg
M1=2kg
M2=1kg
M2=1kg
Two blocks collide and bounce apart, what is their final velocity?

10. Example: collision “before” “after”
Vo = 3m/s
Vo = 3m/s
M1=2kg
M1=2kg
M2=1kg
M2=1kg
Two blocks collide and bounce apart, what is their final velocity?

11. Summary Collisions and Explosions Center of Mass (Balance Point)
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