1. Objectives Students should be able to: 1. Define linear momentum and calculate it. 2. Define and calculate impulse and apply it in the relationship, FΔt = mΔv. 3. Apply the concept of impulse to various situations. 4. design an experiment in order to make conclusions about the total momentum in a system before and after a collision or explosion.

2. Let’s start with everyday language What do you say when a sports team is on a roll? They may not have the lead but they may have ___________ MOMENTUM A team that has momentum is hard to stop.

3. Momentum Defined p = m v p = momentum vector m = mass v = velocity vector

4. Momentum Momentum depends on the mass of an object and the speed it is going. –Momentum = mass x velocity Because velocity has direction then momentum does, also.

5. Momentum of Objects Put the following in the order of most momentum to least: –Mosquito –Automobile –Space Shuttle –Bullet –Freight Train

6. Questions Does a small object always have less momentum than a large one? How can a bullet from a rifle knock over an animal?

7. Which has more momentum? A truck or a roller skate rolling down a hill with the same speed? A truck stopped at a light or a marble rolling down the road? When could the roller skate and the truck have the same momentum?

8. What is Momentum? An object with a lot of momentum is also hard to stop Momentum = ρ = mv Units: kg∙m/s m=mass v=velocity Momentum is also a vector (it has direction)

9. Momentum  Momentum is _________ in ________.  Momentum is a vector quantity.  Momentum is dependant on the mass and the ___________ of an object. MASS MOTION VELOCITY

10. Momentum Facts p = m v Momentum is a vector quantity! Velocity and momentum vectors point in the same direction. SI unit for momentum: kg · m /s (no special name). Momentum is a conserved quantity (this will be proven later). A net force is required to change a body ’ s momentum. Momentum is directly proportional to both mass and speed. Something big and slow could have the same momentum as something small and fast.

11. Momentum Examples 10 kg 3 m /s 10 kg 30 kg · m /s Note: The momentum vector does not have to be drawn 10 times longer than the velocity vector, since only vectors of the same quantity can be compared in this way. 5 g 9 km /s p = 45 kg · m /s at 26º N of E 26º

12. Equivalent Momenta Bus: m = 9000 kg; v = 16 m /s p = 1.44 ·10 5 kg · m /s Train: m = 3.6 ·10 4 kg; v = 4 m /s p = 1.44 ·10 5 kg · m /s Car: m = 1800 kg; v = 80 m /s p = 1.44 ·10 5 kg · m /s continued on next slide

13. Equivalent Momenta (cont.) The train, bus, and car all have different masses and speeds, but their momenta are the same in magnitude. The massive train has a slow speed; the low-mass car has a great speed; and the bus has moderate mass and speed. Note: We can only say that the magnitudes of their momenta are equal since they ’ re aren ’ t moving in the same direction. The difficulty in bringing each vehicle to rest--in terms of a combination of the force and time required--would be the same, since they each have the same momentum.

14. January 31, 2016 Newton’s Law and Momentum Newton’s Second Law can be used to relate the momentum of an object to the resultant force acting on it The change in an object’s momentum divided by the elapsed time equals the constant net force acting on the object

15. Problem  A 1200 kg car drives west at 25 m/s for 3 hours. What is the car’s momentum?  Identify the variables: 1200 kg = m 25m/s, west = v 3 hours = t p = mv p = (1200kg)(25m/s) = 30000 kgm/s, west

16. Class work/Homework The Physics Classroom- Hand-out and on computer (Ask for this hand-out if you want it as an optional assignment.) Impulse, Momentum, and Change in Momentum (Ask for this hand-out and finish for homework.)