Physics 103: Lecture 11 Chapter 6 Impulse and Momentum

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Physics 103 Lecture 11Chapter 6Impulse and
Momentum
Exam I results posted at http//tycho.physics.wisc
.edu/courses/phys103/fall09/exams.html
Mean 63 - 15

• Todays lecture will cover the following new
  concepts
• Momentum
• Impulse
• Impulse-Momentum Theorem
• Momentum Conservation

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Momentum

• The linear momentum of an object of mass m
  moving with a velocity is defined as the
  product of the mass and the velocity
• SI Units are kg m / s
• Vector quantity, the direction of the momentum is
  the same as the velocitys
• Applies to two, three-dimensional motion

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Impulse and Momentum

• Impulse average force ? time
• I Fave ?t ?P

(not necessary)
Assumption mass m of the object is constant
Kinetic energy gt Work Momentum gt Force
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Questions
You drop an egg onto a) the floor b) a thick
piece of foam rubber In both cases, the egg does
not bounce. In which case is the impulse
greater? A) case 1 B) case 2 C) the same
In which case is the average force greater A)
case 1 B) case 2 C) the same
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Preflight Questions 2 3

• Two identical balls are dropped from the same
  height onto the floor. In case 1 the ball bounces
  back up, and in case 2 the ball sticks to the
  floor without bouncing. In which case is the
  impulse given to the ball by the floor larger?
• 1. Case 1
• 2. Case 2
• 3. The same

the impulse is greater for case 1 because the
change in momentum of the object is proportional
to the change in velocity which is greater in
case 1 because it has a greater final velocity
(down then up) than case 2 (which is only from
down to zero). Impulse must be greater for case
1.
Example suppose m1 kg, v(initial)-1
m/s mv(initial) -1 kg-m/s Case 1 mv(final)
1 kg-m/s Impulse 1- (-1)2 Case 2
mv(final) 0 Impulse 1 - 0 1 Note
the direction (upward) important.
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Preflight Lecture 10 No.1

•  The impulse delivered to a body by a force is
• defined only for interactions of short duration.
       
• equal to the change in momentum of the body.
       
• equal to the area under an F versus x graph.
       
• defined only for elastic collisions.

• 1 Often useful in this situation, but not ONLY

• 3 Equal to the area under an F versus t graph!

• 4 it is defined for all collisions elastic
  inelastic!

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Preflight Questions 6, 7 8

• Is it possible for a system of two objects to
  have zero total momentum while having a non-zero
  total kinetic energy?
• 1. YES
• 2. NO

in an isolated system, two ice skaters starting
at rest and pushing on one another will move in
opposite directions thus the momenta of the two
are equal and opposite and total momentum is
zero. but they are moving apart after the push
and therefore the KE is non-zero.
two hockey pucks moving towards each other with
the same speed on a collision course have zero
total momentum, but a non zero total kinetic
energy
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Momentum Conservation

• Momentum-Impulse Theorem
• Fave?t ? I pf - pi ?p
• If F 0 ? momentum conserved (?p 0)

• For a collection of objects, the total net force
• Fext 0 ? total momentum conserved

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Some Terminology

• Elastic Collisions
• collisions that conserve kinetic energy
• Inelastic Collisions
• collisions that do not conserve kinetic energy
• Completely Inelastic Collisons
• objects stick together
• or an object breaks up into
  pieces

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Elastic Collision in 1-Dimension
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Elastic Collision
Magnitude of relative velocity is conserved.
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Preflight Lecture 10 No.9

• In an elastic collision      
• kinetic energy is conserved.      
• momentum is conserved.      
• the magnitude of the relative velocity is
  conserved.      
• all of the above are correct.

• 1 True by definition of elastic

• 2 True by definition of collision

• 3 Total momentum is unchanged

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Preflight Lecture 10 No.10

• In an inelastic collision      
• both kinetic energy and momentum are conserved.
       
• only kinetic energy is conserved.      
• only momentum is conserved.      
• neither kinetic energy nor momentum are
  conserved.

• 1 False by definition of inelastic collision

• 2 False by definition of inelastic collision

• 4 False by definition of collision

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Collisions
Procedure

• Draw before, after
• Define system so that Fext 0
• Set up axes
• Compute Ptotal before
• Compute Ptotal after
• Set them equal to each other

Explosions
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Explosions

• Example m1 M/3 m2 2M/3
• Which block has larger momentum?
• Each has same momentum
• Which block has larger velocity?
• mv same for each ? smaller mass has
  larger velocity
• Which block has larger kinetic energy?
• KE mv2/2 m2v2/2m p2/2m ? smaller mass has
  larger KE
• Is kinetic energy conserved?

• NO!!

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Totally Inelastic Head-on Collision
Draw before and after
before
System two blocks

• Before Ptotal,before mv (-mv) 0 !
• After Ptotal,after (2m)vf
• Ptotal,before Ptotal,after
• 0 (2m)vf
• vf 0 !
• Therefore KEafter 0

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Preflight Question 11 12

• Movies often show someone firing a gun loaded
  with blanks. In a blank cartridge the lead bullet
  is removed and the end of the shell casing is
  crimped shut to prevent the gunpowder from
  spilling out. When a gun fires a blank, is the
  recoil greater than, the same as, or less than
  when the gun fires a standard bullet?
• 1. greater than
• 2. same as
• 3. less than

Impulse is the same in the two cases
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Reprise
1a) Momentum is mass times velocity (vector).
1b) Impulse (vector) is average force times time
of action (equal to the momentum change.)

• Momentum is conserved when no external force.

• Kinetic energy may be conserved (elastic
  collisions)
• or may not (inelastic collisions).

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Conceptual Example

• Consider two blocks (mass m and M) sliding toward
  one another (with velocities vm and vM) on a
  frictionless plane.

vM
vm
M
m
What happens after the collision?
What does your result depend on?
Is the collision elastic or? Kinetic energy loss
in inelastic!
How would the answer change if there was friction
between the blocks and the plane?
Kinetic energy would be lost during the motion.
We would need initial distances to calculate!