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Chapter 6: Momentum and Collisions

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Chapter 6: Momentum and Collisions Objectives Understand the concept of momentum. Use the impulse-momentum theorem to solve problems. Understand how time and force ... – PowerPoint PPT presentation

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Title: Chapter 6: Momentum and Collisions


1
Chapter 6 Momentum and Collisions
2
Objectives
  • Understand the concept of momentum.
  • Use the impulse-momentum theorem to solve
    problems.
  • Understand how time and force are related in
    collisions.

3
Momentum
momentum inertia in motion the product of mass
and velocity
p m v
How much momentum does a 2750 kg Hummer H2
moving at 31 m/s possess?
Note momentum is a vector units are kgm/s
4
Impulse Changes Momentum
Newton actually wrote his second law in this form
SF Dt m Dv
The quantity SFDt is called impulse.
The quantity mDv represents a change in momentum.
Thus, an impulse causes a change in momentum
SF
SFDt mDv Dp
impulse-momentum theorem
5
Highway Safety and Impulse
Water-filled highway barricades increase the time
it takes to stop a car. Why is this safer?
They reduce the force during impact!
SF (m Dv) / Dt
Seatbelts and airbags also increase the stopping
time and reduce the force of impact.
6
Impulse Problem
  • A car traveling at 21 m/s hits a concrete wall.
    If the 72 kg passenger is not wearing a seatbelt,
    he hits the dashboard and stops in 0.13 s.
  • What is the Dp?
  • How much impulse is applied to the passenger?
  • How much force does the
  • dashboard apply to the passenger?

What is the force applied to the passenger if he
is wearing a seatbelt takes 0.62 s to stop?
7
Impulse Problem
The face of a golf club applies an average force
of 5300 N to a 49 gram golf ball. The ball
leaves the clubface with a speed of 44 m/s. How
much time is the ball in contact with the
clubface?
SFDt mDv
SF
8
Bouncing
Which collision involves more force a ball
bouncing off a wall or a ball sticking to a wall?
Why?
The ball bouncing because there is a greater Dv.
SF Dt m Dv
SF Dv
so
Pelton wheel
9
Objectives
  • Understand the concept of conservation of
    momentum.
  • Understand why momentum is conserved in an
    interaction.
  • Be able to solve problems involving collisions.

10
Conservation of Momentum
conservation of momentum in any interaction
(such as a collision) the total combined
momentum of the objects remains unchanged (as
long as no external forces are present).
system all of the objects involved in an
interaction
11
system
Conservation of Momentum
mavai mbvbi Spi
mb
ma
vai
vbi
SF
-SF
-Dp -SF Dt
Dp SF Dt
Dt
DpTOTAL ( -SFDt ) ( SFDt ) 0
mavaf mbvbf Spf
mb
ma
S pi S pf
vaf
vbf
Law of Conservation of Momentum
mavai mbvbi mavaf mbvbf
12
Slingshot Manuever
The spacecraft is pulled toward Jupiter by
gravity, but as Jupiter moves along its orbit,
the spacecraft just misses colliding with the
planet and speeds up.
The spacecraft substantially increased its
momentum (as speed) and Jupiter lost the same
amount of momentum, but because Jupiter is so
massive, its overall speed remained virtually
unchanged.
Jupiter
S pi S pf
13
Conservation of Momentum Problem
A 0.85 kg bocce ball rolling at 3.4 m/s hits a
stationary 0.17 kg target ball. The bocce ball
slows to 2.6 m/s. How fast does the target ball
(pallino) move? Assume all motion is in one
dimension.
mavai mbvbi mavaf mbvbf
14
Objectives
  • Understand the difference between elastic and
    inelastic collisions.
  • Solve problems involving conservation of momentum
    during an inelastic collision.

15
Collisions
  • elastic objects collide and rebound, maintaining
    shape
  • both KE and p are conserved (DEMONewton spheres)
  • perfectly inelastic objects collide, deform, and
    combine into one mass
  • KE is not conserved (becomes sound, heat, etc.)
  • real collisions are usually somewhere in between

16
Types of Collisions
elastic
mavai mbvbi mavaf mbvbf
perfectly inelastic
mavai mbvbi (ma mb) vf
17
Conservation of Momentum Problem
Victor, who has a mass of 85 kg, is trying to
make a get-away in his 23-kg canoe. As he is
leaving the dock at 1.3 m/s, Dakota jumps into
the canoe and sits down. If Dakota has a mass
of 64 kg and she jumps at a speed of 2.7 m/s,
what is the final speed of the the canoe and its
passengers?
18
Conservation of Momentum in Two-Dimensions
Collisions in 2-D involve vectors.
paf
ma
initial
ma
mb
final
Spi
mb
pbf
19
Equal Mass Collision
A cue ball (m 0.16 kg) rolling at 4.0 m/s hits
a stationary eight ball of the same mass. If the
cue ball travels 25o above its original path and
the eight ball travels 65o below the original
path, what is the speed of each ball after the
collision?
20
Unequal Mass Collision
A 0.85 kg bocce ball rolling at 3.4 m/s hits a
stationary 0.17 kg target ball. The bocce ball
slows to 2.8 m/s and travels at a 15o angle above
its original path. What is the speed of the
target ball it travels at a 75o below the
original path?
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