Chapter 7 71 The ImpulseMomentum Theorem This section deals with timevarying forces affecting the motion of objects The effects of these forces will be discussed using the concepts of i mpulse and linear momentum ID: 301900
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Slide1
Impulse and Momentum
Chapter 7Slide2
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.htmSlide3
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 directionSI Unit: Newton •second (N•s)Slide4
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!Slide5
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)Slide6
Impulse-Momentum Theorem
By combining what we know about Newton’s 2
nd
Law, impulse, and momentum we can derive the Impulse-Momentum TheoremSlide7
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!Slide8
Example: A Rainstorm (pg. 199)
During a storm, rain comes down with a velocity of v
0
= -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.
Slide9
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!Slide10
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.Slide11
Internal vs. 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 resisitanceInternal
ExternalSlide12
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.Slide13
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.Slide14
Types of Collisions
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.
Elastic
Inelastic
Give examples of elastic, inelastic, and completely inelastic collisions!Slide15
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 vSlide16
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.
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.
To find the velocity of the center of mass use the equation…Slide17
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, practiceBe careful of signs!