Classical Mechanics
Lecture 11
Today’s Concept:
Conservation of Momentum
Inelastic Collisions
Mechanics Lecture 11, Slide 1
Midterm Exam 2
Average = 5.6
 Please re-submit a response booklet with answers marked on front
page and work shown in booklet. You need only answer the problems
that were marked incorrect on your exam booklet that was returned
today (11/11/13). The re-submitted exam is due by the lecture on Friday
November 15.
 Partial credit will be added to the score of your original exam
(submitted on November 8) and then averaged with the exam that you
re-submit on November 15.
Mechanics Lecture 11, Slide 2
Homework Unit 10
Average = 81%
Several students not
doing homework!
Mechanics Lecture 11, Slide 3
Main Points
Mechanics Lecture 11, Slide 4
Main Points
Mechanics Lecture 11, Slide 5
Conservation of Momentum
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Mechanics Lecture 11, Slide 6
Mechanics Lecture 11, Slide 7
Conservation of Total Momentum
Mechanics Lecture 11, Slide 8
Conservation of Total Momentum
Mechanics Lecture 11, Slide 9
Total Momentum & Center of Mass
Mechanics Lecture 11, Slide 10
Conservation of Total Momentum
Mechanics Lecture 11, Slide 11
Example
Mechanics Lecture 11, Slide 12
Example
Mechanics Lecture 11, Slide 13
Example
Mechanics Lecture 11, Slide 14
Momentum in 2-d
More about this later…
Mechanics Lecture 11, Slide 15
Collisions: Conservation of Total Momentum
Mechanics Lecture 11, Slide 16
Collision and Momentum Conservation
Mechanics Lecture 11, Slide 17
Checkpoint
A.
B.
C.
0%
0%
0%
Mechanics Lecture 11, Slide 18
Checkpoint
Mechanics Lecture 11, Slide 19
Inelastic Collisions
 Internal forces do not affect conservation of momentum !
 Kinetic Energy of Center of Mass motion also unchanged
 However sum of Kinetic Energy of individual element
may be reduced
Mechanics Lecture 11, Slide 20
Collisions:Kinetic Energy
Mechanics Lecture 11, Slide 21
Collisions: Kinetic Energy
Mechanics Lecture 11, Slide 22
Inelastic Collision
Mechanics Lecture 11, Slide 23
Which Kinetic Energy ?
Mechanics Lecture 11, Slide 24
Energy loss in collision
Mechanics Lecture 11, Slide 25
Center of Mass Frame
Mechanics Lecture 11, Slide 26
Center of Mass Frame
Mechanics Lecture 11, Slide 27
Mechanics Lecture 11, Slide 28
Mechanics Lecture 11, Slide 29
A.
Checkpoint
B.
C.
0%
0%
0%
Mechanics Lecture 11, Slide 30
Mechanics Lecture 11, Slide 31
What is the different between conservation of Momentum and
conservation of energy? How do I know if the Momentum is
conserve or energy is conserve?
Momentum (Prelecture 11)
Energy (Prelecture 8)
Mechanics Lecture 11, Slide 32
Clicker Question
A.
B.
C.
D.
E.
A wood block rests at rest on a table. A bullet shot into
the block stops inside, and the bullet plus block start sliding on the
frictionless surface. The momentum of the bullet plus block remains
constant
Before
A) Before the collision.
B) During the collision
C) After the collision
D) All of the above
E) Only A and C above
After
20%
20%
20%
20%
20%
As long as there are no external forces
acting on the system
Mechanics Lecture 11, Slide 33
Recap


Ptot   mi vi
i
Mechanics Lecture 11, Slide 34
CheckPoint
Suppose you are on a cart initially at rest that rides on a frictionless
track. If you throw a ball off the cart towards the left, will the cart be
put into motion?
Left
Right
A) Yes, and it moves to the right.
B) Yes, and itofmoves
to the
left. the cart must
Conservation
momentum
means
move
right since
the ball moves to the left.
C) No,toitthe
remains
in place.
Mechanics Lecture 11, Slide 35
CheckPoint
Suppose you are on a cart which is initially at rest that rides on a
frictionless track. You throw a ball at a vertical surface that is firmly
attached to the cart. If the ball bounces straight back as shown in
the picture, will the cart be put into motion after the ball bounces
back from the surface?
Left
Right
A) Yes, and it moves to the right.
B) Yes, and it moves to the left.
C) No, it remains in place.
Mechanics Lecture 11, Slide 36
Clicker Question
A.
B.
C.
Suppose you are on a cart that is moving at a constant speed v toward
the left on a frictionless track. If you throw a massive ball straight up
(relative to the cart), how will the speed of the cart change?
Left
Right
33%
33%
33%
v
A) Increase
B) Decrease
C) Will not change
As long as there are no external forces
acting on the system, Ptotal is conserved
Mechanics Lecture 11, Slide 37
CheckPoint
Two balls of equal mass are thrown horizontally with
the same initial velocity. They hit identical stationary
boxes resting on a frictionless horizontal surface.
The ball hitting box 1 bounces back, while the ball
hitting box 2 gets stuck.
Which box ends up moving faster?
A) Box 1
B) Box 2
1
C) same
2
Mechanics Lecture 11, Slide 38
CheckPoint
Which box ends up moving faster?
A) Box 1
B) Box 2
C) same
1
2
A) As the ball bounces to the left, cart 1 moves faster to the right to
conserve momentum.
B) Some of the energy is not transferred to
box 1, since the ball bounces back
C) The starting velocity and mass is all the
same so the momentum will be the same in
both cases.
Think of a 2-step “bounce”
Mechanics Lecture 11, Slide 39
A.
Clicker Question
B.
C.
Two equal-mass balls swing down and hit identical bricks while
traveling at identical speeds. Ball A bounces back, but ball B just
stops when it hits the brick. Which ball is more likely to knock the
brick over?
33%
A
33%
33%
B
A) A
B) B
C) They both have the same chance.
Mechanics Lecture 11, Slide 40
demo
B
A
DPA
DPB
DPA > DPB
The change in the momentum of the ball is bigger in A
Mechanics Lecture 11, Slide 41
Ballistic Pendulum
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html
Mechanics Lecture 11, Slide 42
Ballistic Pendulum
m
v
M
H
A projectile of mass m moving horizontally with speed v strikes a
stationary mass M suspended by strings of length L.
Subsequently, m + M rise to a height of H.
Given H, what is the initial speed v of the projectile?
Mechanics Lecture 11, Slide 43
Breaking it down into steps
before
during
after
V
m
v
M
H
splat
Which quantities are conserved before the collision?
A) momentum
B) mechanical energy
C) both momentum and mechanical energy
Mechanics Lecture 11, Slide 44
Breaking it down into steps
before
during
after
V
m
v
M
H
splat
Which quantities are conserved during the collision?
A) momentum
B) mechanical energy
C) both momentum and mechanical energy
m v  (m  M )V
Mechanics Lecture 11, Slide 45
Breaking it down into steps
before
during
after
V
m
v
M
H
splat
Which quantities are conserved after the collision
A) momentum
B) mechanical energy
C) both momentum and mechanical energy
V 2  2 gH
Mechanics Lecture 11, Slide 46
Ballistic Pendulum
m
v
M
m v  (m  M )V
V  2 gH
H
m
V
v
(m  M )
2
mM 
v  2 gH 

 m 
 M
v  2 gH 1  
m

Mechanics Lecture 11, Slide 47
Ballistic Pendulum
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html
Mechanics Lecture 11, Slide 48