Conservation of Momentum

1
Conservation of Momentum

• For next time
• Read Chapter 7, Section 5
• Homework
• Chap 7, Problem 46 (16 in old)
• SP 65, SP 66

2
SP 67
Dp FaveDt
5 Fave(0.02)
3 Francii
3
When do I use momentum?
Dt 0.1s
1m
4
Truck hits Volvo
or, Volvo hits truck.
5
During the collision
What is the total impulse for the truck-Volvo
system?
6
During the collision
What is the total impulse for the truck-Volvo
system?
ImpulseTOTAL ImpulseTRUCK ImpulseVOLVO
7
Free-Body Diagrams
ImpulseTOTAL ImpulseTRUCK ImpulseVOLVO
8
Free-Body Diagrams
NT,V
ImpulseTOTAL ImpulseTRUCK ImpulseVOLVO
9
Free-Body Diagrams
NT,V
NV,T ?t
NT,V ?t
ImpulseTOTAL ImpulseTRUCK ImpulseVOLVO
0
10
What does this say about the change in momentum
of the Truck-Volvo system?
NV,T ?t
NT,V ?t
ImpulseTOTAL ImpulseTRUCK ImpulseVOLVO
0
11
My promise to you

• Always include everything that bumps in your
  system.
• The impulse on your system will then be zero.

12
My promise to you

• Always include everything that bumps in your
  system.
• The impulse on your system will then be zero.

pi pf
13
My promise to you

• Always include everything that bumps in your
  system.
• The impulse on your system will then be zero.

pi (system) pf (system)
14
What is the total kinetic energy of the system?
30 m/s
30 m/s
1200 kg
1200 kg
KEsystem KEleft KEright KEsystem 1/2 ml
vl2 1/2 mr vr2 KEsystem 1/2 (1200)(30)2
1/2 (1200)(-30)2 KEsystem 540,000 J 540,000
J 1,080,000 J
15
What is the total momentum of the system?
30 m/s
30 m/s
1200 kg
1200 kg
psystem pleft pright psystem ml vl mr
vr psystem (1200)(30) (1200)(-30) psystem
36,000 kg m/s (-36,000 kg m/s) 0
16
The momentum of the system cant change so whats
got to happen?
x
30 m/s
30 m/s
1200 kg
1200 kg
psystem pleft pright psystem ml vl mr
vr psystem (1200)(30) (1200)(-30) psystem
36,000 kg m/s (-36,000 kg m/s) 0
17
The momentum of the system cant change so whats
got to happen?
30 m/s
30 m/s
KE 1,080,000 J
1200 kg
1200 kg
KE 0 J
KE 120,000 J
KE 1,080,000 J
18
Where does the energy go?
30 m/s
30 m/s
KE 1,080,000 J
1200 kg
1200 kg
KE 0 J
KE 120,000 J
KE 1,080,000 J
19
Energy has lots of buckets.
30 m/s
30 m/s
KE 1,080,000 J
1200 kg
1200 kg
v0
maximallyinelastic
KE 0 J
10 m/s
10 m/s
inelastic
KE 120,000 J
elastic
KE 1,080,000 J
20
Which collision is most elastic?
21
The two cars lock bumpers after the collision.
30 m/s
0 m/s
1200 kg
1200 kg
elastic inelastic maximally inelastic
Is the final kinetic energy of the system zero?
22
One more time...
A boxcar travelling at 10 m/s approaches a string
of 4 identical boxcars sitting stationary on the
track. The moving boxcar collides and links with
the stationary cars and the five move off
together along the track. What is the final
speed of the five cars immediately after the
collision? (You may take the mass of each boxcar
to be 18537 kg.)
23
One more time...
mcar 18,537 kg