2D Collisions and Center of mass

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

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

Example: shooting pool (cont.)

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

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

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

Elastic Collisions 1. Find V cm. 2. Subtract V cm from both initial velocities. 3. Change sign of both velocities. 4. Add V cm to both velocities.

Example: collision “before” “after” M 1 =2kg M 2 =1kg M 1 =2kg V o = 3m/s V o = 0m/s Two blocks collide and bounce apart, what is their final velocity?

Example: collision “before” “after” M 1 =2kg M 2 =1kg M 1 =2kg V o = 3m/s Two blocks collide and bounce apart, what is their final velocity?

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