Mechanics Lecture 11, Slide 1 Classical Mechanics Lecture 11 Today’s Concept: Conservation of Momentum Inelastic Collisions
Jan 15, 2016
Mechanics Lecture 11, Slide 1
Classical Mechanics Lecture 11
Today’s Concept:Conservation of MomentumInelastic Collisions
Midterm Exam 2
Mechanics Lecture 11, Slide 2
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.
Average = 5.6
Homework Unit 10
Mechanics Lecture 11, Slide 3
Average = 81%
Several students not doing homework!
Main Points
Mechanics Lecture 11, Slide 4
Main Points
Mechanics Lecture 11, Slide 5
Conservation of Momentum
Mechanics Lecture 11, Slide 6
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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
Mechanics Lecture 11, Slide 15
More about this later…
Collisions: Conservation of Total Momentum
Mechanics Lecture 11, Slide 16
Collision and Momentum Conservation
Mechanics Lecture 11, Slide 17
CheckpointA. B. C.
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Checkpoint
Mechanics Lecture 11, Slide 19
Inelastic Collisions
Mechanics Lecture 11, Slide 20
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
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
CheckpointA. B. C.
Mechanics Lecture 11, Slide 30
0% 0%0%
Mechanics Lecture 11, Slide 31
Mechanics Lecture 11, Slide 32
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)
Clicker QuestionA. B. C. D. E.
Mechanics Lecture 11, Slide 33
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A) Before the collision.B) During the collisionC) After the collisionD) All of the aboveE) Only A and C above
Before After
As long as there are no external forces acting on the system
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
Mechanics Lecture 11, Slide 34
Recap
i
iitot vmP
Mechanics Lecture 11, Slide 35
CheckPoint
A) Yes, and it moves to the right.B) Yes, and it moves to the left.C) No, it remains in place.
Left Right
Conservation of momentum means the cart must move to the right since the ball moves to the left.
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?
Mechanics Lecture 11, Slide 36
A) Yes, and it moves to the right.B) Yes, and it moves to the left.C) No, it remains in place.
Left Right
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?
Clicker Question A. B. C.
Mechanics Lecture 11, Slide 37
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Mechanics Lecture 11, Slide 37
A) IncreaseB) DecreaseC) Will not change
v
As long as there are no external forces acting on the system, Ptotal is conserved
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
Mechanics Lecture 11, Slide 38
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 C) same
CheckPoint
1 2
Mechanics Lecture 11, Slide 39
CheckPointWhich box ends up moving faster?
A) Box 1 B) Box 2 C) same
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”
1 2
Clicker QuestionA. B. C.
Mechanics Lecture 11, Slide 40
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A) AB) BC) They both have the same chance.
A B
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?
Mechanics Lecture 11, Slide 41
A B
PA PB
The change in the momentum of the ball is bigger in A
demo
PA > PB
Ballistic Pendulum
Mechanics Lecture 11, Slide 42
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html
Mechanics Lecture 11, Slide 43
Hm
M
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?
v
Ballistic Pendulum
Which quantities are conserved before the collision?
A) momentum B) mechanical energyC) both momentum and mechanical energy
mM
vV
H
before during after
splat
Breaking it down into steps
Mechanics Lecture 11, Slide 44
Which quantities are conserved during the collision?
A) momentum B) mechanical energyC) both momentum and mechanical energy
mM
vV
H
before during after
splat
Breaking it down into steps
Mechanics Lecture 11, Slide 45
VMmmv )(
Which quantities are conserved after the collision
A) momentum B) mechanical energyC) both momentum and mechanical energy
mM
vV
H
before during after
splat
Breaking it down into steps
Mechanics Lecture 11, Slide 46
gHV 22
Hm
Mv
Ballistic Pendulum
Mechanics Lecture 11, Slide 47
VMmmv )(
gHV 22
vMm
mV
)(
m
MmgHv 2
m
MgHv 12
Ballistic Pendulum
Mechanics Lecture 11, Slide 48
http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html