Gaining Momentum:

1. Gaining Momentum: New Vocabulary: Linear Momentum Impulse (force times time) Major Concepts of Chapter 9: • Linear momentum is conserved. It remains the same in the absence of an external force. • Linear momentum can be changed by an impulse (a force acting for a period of time). • Linear momentum is unchanged in collisions • There are two types of collisions: inelastic and elastic. Linear momentum is conserved in BOTH. • An “elastic” collision is one in which the objects “bounce”, and energy is conserved. • An “inelastic” collision is one in which the objects stick together, and energy is lost to heat. Chapter 9

2. Why do we need momentum? • Momentum is useful because it remains unchanged in the absence of external forces • The total momentum of a system of moving objects is the sum of the individual momenta Note that momentum is a VECTOR. It has magnitude AND direction.

3. Momentum changes with an external force. Note: is for the case where mass is constant. This is a more accurate statement of Newton’s second law. An IMPULSE can cause a change in momentum. Check the units: Momentum is mass X velocity = kg – m/s Impulse is mass X acceleration X time = kg-m/s^2 *s

4. Newton’s Second Law Most general form. If mass is constant…. Constant mass form.

5. Changes in momentum. Case A (inelastic collision) Case B (elastic collision) -Pi DP DP Case B Pf Pi Pf

6. Acting on Impulse: Change of Momentum

7. Momentum Conservation • In the absence of an external force, linear momentum of a system of objects does not change. So, if the impulse (external force) is zero, Main Message The total momentum of a system of objects is the sum of the individual momenta.

8. Elastic collision: make a prediction. We will do this experiment in a moment. Assume m1 = m2. If the initial speed is V, what are the final speeds, V1, V2?

9. 0 / 100 Elastic Collision: M1 = M2. The initial velocity of M1 is +V; M2 is zero. The final velocities of M1 and M2, respectively, are: • Zero, V/2 • -V, V • Zero, V • V/2, V/2 Cross-Tab Label

10. Inelastic Collision: Make a prediction

11. Inelastic Collision: M1 = M2. The initial velocity is V. The final velocity is: 0 / 100 • 2V • Zero • V • V/2 Cross-Tab Label

12. 2v M M “Real world.” V A matter of the point of view…. • Imagine how a collision looks, when viewed from a video camera that is moving.

13. 2v M M “Real world.” V Here’s what the film sees…. v v “Film world.” M M Before collision, the film shows two blocks of same mass approaching at the same speed.

14. In the film, two identical masses approach velocity +V and –V respectively. After the collision, the velocity is 0 / 100 • Zero, Zero • -V, +V • -V/2, +V/2 • +V, -V (no change) Cross-Tab Label

15. v v M M Here’s what the film sees…. v v “Film world.” M M Before collision, the film shows two blocks of same mass approaching at the same speed. After the collision, the blocks move apart with equal speed.

16. v v M M If that’s what the film “saw”, what happened in the “real world”?…. “Film world.” After the collision, the blocks move apart with equal speed. V “Real world.” 2v V=0 M M Actually, both situations describe “real” physics. Momentum is conserved in both cases.