2. Summer 2012 PHYS 172: Modern Mechanics Lecture 3 - The Momentum Principle Read 2.1-2.6

3. The Momentum Principle An object moves in a straight line and at constant speed except to the extent that it interacts with other objects The Momentum Principle Change of momentum is equal to the net force acting on an object times the duration of the interaction F net constant during  t! What is “force” F? measure of interaction. defined by the momentum principle.

4. The principle of superposition Net force The Superposition Principle: The net force on an object is the vector sum of all the individual forces exerted on it by all other objects Each individual interaction is unaffected by the presence of other interacting objects Misconception: need constant force to maintain motion Neglected friction! Definition of net force:

5. Impulse The Momentum Principle Definition of impulse Momentum principle: The change of the momentum of an object is equal to the net impulse applied to it Note: small  t F net ~ const

6. Measuring force The Momentum Principle 2. Use the momentum principle 1.Use knowledge of specific Interaction: Hooke’s Law, Gravitational Law, etc. L0L0 L

7. Predictions using the Momentum Principle The Momentum Principle Short enough, F~const For components:

8. Example Force: provided by a spring stretched by  L=4 cm Find momentum p f if p i = kg. m/s 1 second later no friction k S =500 N. m 1. Force: 2. Momentum: NB: force must not change during  t N. s = kg. m/s 2. s = kg. m/s x

9. System and surroundings system System: an object for which we calculate some property (force, momentum, etc) a system can consist of several objects Surroundings: objects which interact with system (earth, man, air…) Only external forces matter ! Internal forces cancel

10. Applying the Momentum Principle to a system: predicting motion 1.Choose system and surroundings 2.Make a list of objects in surroundings that exert significant forces on system 3.Apply the Momentum Principle 4.Apply the position update formula if needed 5.Check for reasonableness (units, etc.)

11. Example: a hockey puck A hockey puck with a mass of 0.16 kg is initially at rest. A player hits it applying force during  t = 4 ms. Where would the puck be 2 seconds after it loses contact with hockey stick? 1.Choose a system and surroundings: Solution:

12. Example: a hockey puck A hockey puck with a mass of 0.16 kg is initially at rest. A player hits it applying force during  t = 4 ms. Where would the puck be 2 seconds after it loses contact with hockey stick? 1.Choose a system and surroundings: Solution: 2. Make a list of objects in surroundings that exert significant forces on system 3. Apply the Momentum Principle Hockey stick Earth Ice (floor) (normal force, ~friction)

13. Example: a hockey puck A hockey puck with a mass of 0.16 kg is initially at rest. A player hits it applying force during  t = 4 ms. Where would the puck be 2 seconds after it loses contact with hockey stick? Solution: 3. Momentum 4. The position update formula * Choose coordinate system origin: initial position of puck x y

14. Clicker question #2: Due to the gravity, which components of the velocity will change? A) x, y and z B)only x and y C)only x D)only y E)only z Constant Gravitational Field x z y

15. Shoot the monkey lecture demo A)Hit the monkey B)Undershoot the monkey C)Overshoot the monkey (ignore air resistance) Note: the trajectory is a parabola (if air friction is ignored) Clicker question #5: The hunter aims right at the monkey and shoots. As the bullet leaves the rifle, the monkey sees the flash and releases the branch entering freefall. Will the bullet: