Impulse and Momentum

1. Impulse and Momentum Chapter 7

2. 7.1 The Impulse-Momentum Theorem • This section deals with time-varying forces affecting the motion of objects. • The effects of these forces will be discussed using the concepts of impulse and linear momentum. Consider this high-speed camera picture of a bat and ball collision. Describe it. To learn more go to http://www.fsus.fsu.edu/mcquone/scicam/ActionReaction.htm

3. Definition of Impulse • The impulse (J) of a force is the product of the average force (F) and the time interval (∆t) during which the force acts: • Impulse is a vector quantity • Direction is the same as average force direction • SI Unit: Newton •second (N•s)

4. Practically Speaking • Large impulses produce large changes in motion. I see… a large average force over a long time period will produce one very large change in a baseball’s motion. But a more massive ball will have a smaller velocity after being hit. Hint for baseball and softball!

5. Linear Momentum • The linear momentum (p) of an object is the product of the object’s mass (m) and velocity (v). • Momentum is a vector quantity • SI Unit: kilogram•meter/second (kg•m/s)

6. Impulse-Momentum Theorem • By combining what we know about Newton’s 2nd Law, impulse, and momentum we can derive the Impulse-Momentum Theorem

7. Impulse-Momentum Theorem • When a net force acts on an object, the impulse of the force is equal to the change in momentum of the object: • Impulse = Change in Momentum **If solving for (F), the force you solve for will be the force that is causing the change in momentum. Be careful when interpreting questions!

8. Example: A Rainstorm (pg. 199) • During a storm, rain comes down with a velocity of v0= -15m/s and hits the roof of a car perpendicularly. The mass of rain per second that strikes the car roof is 0.600kg/s. Assuming that the rain comes to rest upon striking the car, find the average force exerted by the rain on the roof. • Hint: Momentum is a vector! For motion in one dimension, be sure to indicate the direction by assigning a plus or a minus sign to it.

9. Hailstones vs. Raindrops • Just like the happy ball and sad ball, raindrops and hailstones will fall in a very similar manner. • The raindrops will come to a stop after hitting the car roof. Hailstones will bounce. • Given all the same variables for mass, time, and initial velocity, the hailstones will apply a greater force to the roof than the raindrops will. • Make sure you can explain this!

10. 7.2 The Principle of Conservation of Linear Momentum • The impulse-momentum theorem leads to the principle of conservation of linear momentum. • Consider collisions like those discussed in class (baseball, cars, etc). • Collisions will be affected by the mass and velocity of all objects involved in collision. • Internal and External forces acting on the system must also be considered.

11. Internal vs. External Internal External • Forces that the objects within the system exert on each other. • Baseball force on bat, bat force on ball. • Forces exerted on the objects by agents external to the system • Weight of the ball and the bat (weight is a force coming from the Earth) • Friction, air resisitance

12. Conservation of Linear Momentum • In an isolated system (no net external forces are acting), the total momentum before collision is equal to the total momentum after collision. • It is important to realize that the total linear momentum may be conserved even when the kinetic energies of the individual parts of the system change.

13. 7.3 Collisions on One Dimension • There are many different types of collisions and situations to analyze. • Atoms and subatomic particles completely transfer kinetic energy to and from one another. • In “our world”, KE is generally converted into heat or used in creating permanent damage to an object. • Because of the differences in collision types, we categorize them into to main groups.

14. Types of Collisions Elastic Inelastic • One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before collision • The total KE of the system is NOT the same before and after collision. • If the objects stick together after colliding, the collision is called completely inelastic. Give examples of elastic, inelastic, and completely inelastic collisions!

15. 7.4 Collisions in Two Dimensions • Examples of collisions so far have been one dimensional. We have used (+) or (-) in order indicate direction. • We must remember, however, that momentum is a vector quantity and has to be treated as such. • The law of conservation of momentum holds true when objects move in two dimensions (x and y) • In these cases, the x- and y- components are conserved separately. Use vector addition to solve! • Remember: by definition p is in the same direction as v

16. 7.4 Center of Mass • The center of mass (cm) is a point that represents the average location for the total mass of a system. To find the velocity of the center of mass use the equation… If the two masses are equal, it would make sense that the center of mass is ½ way between the particles. If there are more than two masses and they are not aligned in a plane, it would be necessary to find the x- and y- components of the center of mass of each.

17. Helpful websites and hints • Navigate your text website. VERY helpful. • www.physicsclassroom.com (navigate to momentum) • Continue to draw pictures and LABEL EVERYTHING! • Practice, practice, practice • Be careful of signs!