Impulse and Momentum Chapter 7

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

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)

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!

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)

Impulse-Momentum Theorem By combining what we know about Newton’s 2nd Law, impulse, and momentum we can derive the Impulse-Momentum Theorem acceleration Combined with Newton’s 2nd Law The net average force is a change in momentum per unit of time.

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!

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.

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!

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.

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

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.

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.

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!

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

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.

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!