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/Actio
nReaction.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 (Ns)

4
Practically Speaking

• Large impulses produce large changes in motion.

Hint for baseball and softball!
5
Linear Momentum

• The linear momentum (p) of an object is the
  product of the objects mass (m) and velocity
  (v).
• Momentum is a vector quantity
• SI Unit kilogrammeter/second (kgm/s)

6
Impulse-Momentum Theorem

• By combining what we know about Newtons 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!