2. (Linear) Momentum (p) ● Momentum is mass times velocity momentum is a vector! momentum has units kg*m/s Which has more momentum?  1 kg object moving at 1000 m/s -or- a 1000 kg object moving at 1 m/s  a rolling marble –or- stationary truck.  a marble moving at 0.5 m/s –or- truck moving at 0.5 m/s Both have the same momentum! (p = 1000 kg*m/s) The rolling marble has more momentum! A truck has no momentum because it isn’t moving. The truck has more momentum. If two objects are moving at the same speed, the heavier one has more momentum.

3. The way we use the word ‘momentum’ in everyday life actually does relate to its physics definition. In this way, the everyday usage and the physics definition of momentum are the same: Any object with momentum is going to be hard to stop or change. For example, in game, a sports announcer might say that one team ‘has momentum’. What do they mean? The sports announcer means that the team is really on the move and is going to be hard to stop.

4. F∆t = ∆p What is necessary to change an object’s velocity? Force! Changes in momentum are produced by the action of forces of over time. Force applied over time (F∆t) is an called an impulse. units: Ns = kg m/s How do we change momentum? Since mass doesn’t (usually) change, a change in momentum occurs when the velocity of an object changes.  p = mv f - mv i

5. Impulse & momentum  Is it harder to stop an object with more mass or less?  Is it harder to stop a fast moving object or a slow moving object?  Two cars are moving with the same velocity. –In car A, the driver applies the brakes, and the car stops due to the force of friction. The time period over which friction acts is 30 seconds. –Car B hits a tree. The time period over which the tree applies a force is 0.5 seconds. How does the change in momentum of the two objects compare? How does the force applied in each circumstance compare? ∆p = F∆t MORE! Fast-moving!

6. Other examples of minimizing force applied by maximizing time of contact Can you think of any examples?  Air bags  Safety nets used by acrobats  Bending your knees when jumping from heights  Moving with a punch  Wearing boxing gloves

7. Other examples  techniques in karate: increase force by increasing change of momentum  Following through when hitting a ball: This increases change in momentum by increasing the time the force is applied.

8. We do ∆ p = F ∆t ∆ p / F = ∆ t (mv f – mv i ) / F = ∆ t (0.3*80 – 0.3*-60)/350 = 0.12 sec

9. You Do 1)A compact car with mass 725 kg is moving 115 km/hr to the East. The driver suddenly applies the brakes hard for 2.0s, applying an average force of 5.0 X 10 3 N on the car. a) What is the change in momentum of the car? b) What is the final velocity of the car? 2.In a ballistics test at the police department, Officer Rios fires a 6.0 g bullet at 350 m/s into a container that stops it in 0.0018 s. What is the average force that stops the bullet?

10. You Do 1)A compact car with mass 725 kg is moving 115 km/hr to the East. The driver suddenly applies the brakes hard for 2.0s, applying an average force of 5.0 X 10 3 N on the car. a) What is the change in momentum of the car? b) What is the final velocity of the car? 2.In a ballistics test at the police department, Officer Rios fires a 6.0 g bullet at 350 m/s into a container that stops it in 0.0018 s. What is the average force that stops the bullet? 1100 N 10,000 Ns 18 m/s OR 65 km / hr

11. Graphical determination of momentum Change in momentum, Δp, is the area under the graph force vs. time. In the problems we’ve done so far, the we’ve dealt with average or constant force. If force changes over time, we can find the change in momentum graphically. The graph shows the force applied to a 57 g tennis ball by a racquet over time. a)What is the change in momentum? ∆p = area = 1/2b*h = ½* 0.3*6 ∆p = 0.9 Ns b) If the ball starts at rest, what is its final velocity? ∆p = mv f 0.9 / 0.057 = 16 m/s

12. You do: Graphical determination of ∆p a)What is the change in momentum of the football as a result of being kicked? b)If the football started at rest, what is its final velocity? (mass = 400 g)

13. You do: Graphical determination of ∆p a)What is the change in momentum of the football as a result of being kicked? b)If the football started at rest, what is its final velocity? (mass = 400 g) ∆p ≈ 9 Ns v ≈ 23 m/s