1. Momentum Momentum and Collisions Momentum Banging things around…

2. Momentum Impact or product of mass and velocity Impact or product of mass and velocity Impact Represented by the variable “  ” Represented by the variable “  ” Formula  = m v Formula  = m v Units are kg m/s Units are kg m/s

3. MOMENTUM IS MASS TIMES VELOCITY More mass means more impact More mass means more impactmass impactmass impact What has more impact – rolling a pingpong ball or bowling ball? What has more impact – rolling a pingpong ball or bowling ball? More speed means more impact More speed means more impactspeed impactspeed impact what has more impact -catching a tossed ball or line drive? what has more impact -catching a tossed ball or line drive?

4. Impulse The change in momentum The change in momentum Determined by the amount of force for how long Determined by the amount of force for how long Formula is  p= Ft Formula is  p= Ft Classic example is seatbelt vs dashboard. Classic example is seatbelt vs dashboard. Seatbelt means slower stop or less force Seatbelt means slower stop or less force Dashboard means faster stop or more force Dashboard means faster stop or more force

5. Newton’s Laws of Motion Change in momentum occurs when force is applied. 2nd Change in momentum occurs when force is applied. 2nd For every force applied to an object, it applies each force back. 3rd For every force applied to an object, it applies each force back. 3rd

6. Conservation of Momentum Momentum cannot be created or destroyed Momentum cannot be created or destroyed The results of any collision will not change the system momentum The results of any collision will not change the system momentumresults of any collision results of any collision Two objects pushing off each other will have the same total momentum as before the action Two objects pushing off each other will have the same total momentum as before the action

7. Collisions Three types of collisions Three types of collisions Explosions Explosions Inelastic collisions Inelastic collisions Elastic collisions Elastic collisions Momentum is always conserved Momentum is always conserved

8. Explosions Explosions are collisions where the objects begin as one and then separate into many objects traveling in different directions. Explosions are collisions where the objects begin as one and then separate into many objects traveling in different directions. All collisions begin with determining the masses involved in the collision. We designate these as m 1 and m 2. All collisions begin with determining the masses involved in the collision. We designate these as m 1 and m 2. In an explosion, these two masses are added together before the explosion. And counted separately after the explosions. In an explosion, these two masses are added together before the explosion. And counted separately after the explosions.

9. After the Explosion… The sum of the momentums after the explosion must equal the sum of the momentums before the explosion. The sum of the momentums after the explosion must equal the sum of the momentums before the explosion. (m 1 + m 2 )v = m 1 v 1 + m 2 v 2 Don’t forget positive and negative directions.

10. Example #1 A 40-kg boy is sitting on a frozen pond holding a 4-kg book. The ice is very slick and he cannot get off the ice. If he throws the book at 6 m/s. How fast will he travel in the opposite direction? M 1 = 40 kg M 2 = 4 kg M T = 44 kg V 2 = 6 m/s v T = 0 m/s V 2 = 6 m/s v T = 0 m/s (m 1 + m 2 )v T = m 1 v 1 + m 2 v 2

11. Inelastic collisions Objects collide and continue as one object – joined like two trains hooked together or a receiver catching a football. Objects collide and continue as one object – joined like two trains hooked together or a receiver catching a football. Formula is Formula is m 1 v 1 + m 2 v 2 = (m T )v T

12. Example #2 Sante throws a 20-kg medicine ball at 10 m/s to his friend Frankie weighing a hefty 100 kgs who is moving away from Sante at 2 m/s. Somehow, Santee catches the ball and falls forward. What speed does he fall forward? Sante throws a 20-kg medicine ball at 10 m/s to his friend Frankie weighing a hefty 100 kgs who is moving away from Sante at 2 m/s. Somehow, Santee catches the ball and falls forward. What speed does he fall forward? M 1 = 20 kg M 2 = 100 kg M T = 120 kg V1= 10 m/s V 2 = 2 m/s v T = ? m/s

13. Elastic collisions Objects collide and then bounce off each other. Objects collide and then bounce off each other. Formula is: Formula is: m 1 v 1 + m 2 v 2 = m 1 v 1 ’ + m 2 v 2 ’

14. Example #3 Two 200 kg bumper cars race towards each other at 10 m/s and 15 m/s. After the bump, the slower car moves away at a velocity of 12 m/s. What is the velocity of the faster car? m 1 = 200kgm 2 = 200 kg V1 = 10 m/s v2 = -15 m/s V1’ =