Physics 211
Lecture 11
Today’s Concept:
Inelastic Collisions
Mechanics Lecture 11, Slide 1
Hour Exam 1
High Score of 92%
Charles Huh
Yixin Yu
Mean score of 75.1%
Mechanics Lecture 11, Slide 2
Hour Exam 1
High Score of 92%
Charles Huh
Yixin Yu
Mean score of 75.1%
Repeat of an important tip:
Never write an equation
before making a diagram.
Don’t do anything before
making a diagram.
Diagrams are important.
Mechanics Lecture 11, Slide 3
What is the difference between conservation of Momentum and
conservation of energy? How do I know if the Momentum is
conserved or energy is conserved?
Momentum (Prelecture 11)
Energy (Prelecture 8)
Demos: Newton’s cradle,
Happy/sad balls
Mechanics Lecture 11, Slide 4
Collisions
Ptot   mi vi
i
Demo: Inelastic collision on air track
Mechanics Lecture 11, Slide 5
ACT
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. Which of the following (for the bullet+block
system) remain constant during the collision?
Before
A) Horizontal momentum
B) Kinetic energy
C) Both of the above.
D) Neither.
After
As long as there are no external forces
acting on the system
Mechanics Lecture 11, Slide 6
Homework Problem
p1
p2
pinit
p2
p1
pfinal
q
Mechanics Lecture 11, Slide 7
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 it
to the
left. the cart must
Conservation
ofmoves
momentum
means
move
toitthe
right since
the ball moves to the left.
C) No,
remains
in place.
Mechanics Lecture 11, Slide 8
????
Tell me more
Tell me more
Why? Why not? Tell me more
Mechanics Lecture 11, Slide 9
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 10
CheckPoint
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 11
“spot on”
“spot on”
Great observation!
“spot on”
“other”?
???
!!!!!
!!!!!
What’s the final result?
Which direction is “back”?
Left? Good.
Great observation!
Mechanics Lecture 11, Slide 12
ACT
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
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 13
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 14
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 15
The beginning of understanding.
Momentum is also conserved in the first case.
I don’t know how to dissipate momentum.
Is “more conserved” like “more equal”?
But the collisions are not identical.
?????
?????
True. How does that affect this?
No.
No.
Mechanics Lecture 11, Slide 16
ACT
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?
A
B
A) A
B) B
C) They both have the same chance.
Mechanics Lecture 11, Slide 17
B
A
DPA
DPB
DPA > DPB
The change in the momentum of the ball is bigger in A
Demo: super/clay ball pendulum
Mechanics Lecture 11, Slide 18
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?
Show us a difficult problem that would involve momentum.
Mechanics Lecture 11, Slide 19
Breaking it down into steps
before
during
after
v
m
v
M
H
splat
Which quantities are conserved before the collision?
A) momentum (horizontal)
B) mechanical energy
C) both momentum and mechanical energy
Mechanics Lecture 11, Slide 20
Breaking it down into steps
before
during
after
v
m
v
M
H
splat
Which quantities are conserved during the collision?
A) Momentum (horizontal)
B) mechanical energy
C) both momentum and mechanical energy
mv  ( m  M )V
Mechanics Lecture 11, Slide 21
Breaking it down into steps
before
during
after
v
m
v
M
H
splat
Which quantities are conserved after the collision
A) momentum (horizontal)
B) mechanical energy
C) both momentum and mechanical energy
V 2  2 gH
Mechanics Lecture 11, Slide 22
Ballistic Pendulum
m
v
M
mv  (m  M )V
H
m
V
v
(m  M )
V 2  2 gH
mM 
v  2 gH 

m


 M
v  2 gH 1  
 m
Mechanics Lecture 11, Slide 23
Ballistic Pendulum Demo
L
L
m
v
L
L
M
H
Mm
d
In the demo we measure forward displacement d, not H:
L
L- H
H
d
L2  d 2  ( L - H )2
H  L - L2 - d 2
v(mph)  3d(cm)
 M g
v  1   d
 m L
for d << L
Physics 211 Lecture 11, Slide 24
Final thoughts
Have we covered these?
Mechanics Lecture 11, Slide 25