2 D Collisions and Center of mass y

2 D Collisions and Center of mass

y Collisions or Explosions in Two Dimensions x before after • Ptotal, x and Ptotal, y independently conserved Ptotal, x, before = Ptotal, x, after Ptotal, y, before = Ptotal, y, after 37

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

Example: shooting pool (cont. )

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

Example: center of mass 1 m m = 0. 140 kg 0. 1 m M= 0. 515

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

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

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

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

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