2. Defining Systems : Has 2 interacting objects, defined for a problem, and is closed and isolated Closed: mass is constant Isolated: no external force

3. Sum of the initial momentum (p) of the system must equal the sum of the final momentum (p) of the system. momentum lost by one object must equal gain By other object *Momentum before interaction = Momentum after interaction* Initial = Final p i = p f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f Initial = Final p i = p f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f

4. Total momentum AND total Kinetic Energy (KE) of system is conserved: Objects “bounce” off each other, and the object with greater KE transfers some or all of its KE to the other object

5. A blue train car with a mass of 1 kg and a velocity of 2 m/s collides elastically with a stationary green train car with a mass of 1 kg. What is the velocity of the green train car after the collision? m 1 v 1 = m 2 v 2 (1)(2) = (1)v 2 ; v 2 = 2 m/s

6. A blue train car with a mass of 1 kg and a velocity of 2 m/s collides elastically with a green train car with a mass of 1 kg and a velocity of 1 m/s. After the collision, the blue car moves with a velocity of 1 m/s. What is the velocity of the green train car after the collision? Initial = final m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f (1)(2) + (1)(1) = (1)(1) + (1)v 2f 3 = 1 + v 2 v 2f = 2 m/s

7. Total momentum of system is conserved, but KE converts to other kinds of energy Objects stick together m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f

9. A blue train car with a mass of 1 kg and a velocity of 2 m/s collides inelastically with a stationary green train car with a mass of 1 kg. What is the velocity of the stuck-together train cars after the collision? m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f (1)(2) + (1)(0) = (1 + 1) v f 2 = 2 v f v f = 1 m/s

10. Would it be a good idea to jump from a rowboat to a dock that seems within jumping distance? Explain. Hint 1: Is the object you’re jumping from stationary? Hint 2: What will be the final position of the rowboat? Answer : Bad idea ! When you jump the boat will push you forward, but you will push the boat backward. You ’ ll make it to the dock, but the rowboat will be adrift.

11. Rockets are unable to accelerate in space because: A. There is no air in space for the rocket to push against. B. There is no gravity in space. C. There is no air resistance in space. D. Nonsense! Rockets do accelerate in space!

12. Initial momentum of entire system is zero (neither object has KE) The interaction between the two objects must be equal and opposite A 2 kg rocket zooms upward at 5 m/s. It is propelled by 1 kg of water shooting downward. How fast does the water shoot out? Momentum Rocket = Momentum Exhaust Momentum Rocket = Momentum Exhaust

13. Initial momentum of entire system is zero (neither object has KE) The interaction between the two objects must be equal and opposite A 2 kg rocket zooms upward at 5 m/s. It is propelled by 1 kg of water shooting downward. How fast does the water shoot out? 0 kg·m/s = m 1 v 1f + m 2 v 2f