10/21 Momentum Intro

1
10/21 Momentum Intro

• Text Chapter7
• Lab Momentum
• HW None Assigned, read Ch 7 instead

2
What do you think?
A hits block X
A hits block Y
v 0
v 0
Velocities before collision are the same in both
cases
X
A
A
Y
X and Y both have the same mass but X must be
made of a more elastic or more bouncy material.
Which block, X or Y, has the greater velocity
after the collision?
3
What do you think?
v 0
v 0
Velocities before collision are the same in both
cases
X
A
A
Y
v 0
A rebounds off of X but does not rebound off of Y
A
A
Y
X
Student 1 I say Y since block A stops dead in
that case, giving all its momentum to Y.
Student 2 I say X since block A turns around
so it must have had a greater net force on it.
Student 1 But we are talking about X and Y,
not A!
Student 2 But the 3rd law says that the net
force on A equals the net force on the other
block.
4
What do you think?
v 0
v 0
Velocities before collision are the same in both
cases
X
A
A
Y
v 0
A rebounds off of X but does not rebound off of Y
A
A
Y
X
Lets check into Student 2s idea. In either
collision, the FBDs look like
Student 1 Well, so what. The force only lasts
for a millisecond, and without knowing ?t you
cant find ?v anyway! Pbtbthtbthtbt!!!!!
Student 2 Oh yeah? WellwellI itsbut...
Darn!
5
What do you think?
v 0
v 0
Velocities before collision are the same in both
cases
X
A
A
Y
v 0
A rebounds off of X but does not rebound off of Y
A
A
Y
X
Poor Student 2! Lets see if we really need ?t
to find ?v.
The Fnets are equal and opposite for A and B and
the ?ts are the same for A and B (contact time)
so...
A
B
NB,A
NA,B
The product Fnet?t must be equal and opposite for
A and B and also the product m?v must be equal
and opposite for A and B.
6
Momentum
Symbol p
We work with the initial momentum, final
momentum, and the change in momentum.
7
Student 2s revenge
v 0
v 0
Velocities before collision are the same in both
cases
X
A
A
Y
v 0
A rebounds off of X but does not rebound off of Y
A
A
Y
X
Student 2 By golly Ive got it now! The change
in momentum of A is equal and opposite to the
change in momentum of a block! We dont
need to know ?t! neener neener neener!
X is faster than Y!
8
Lab Linear Momentum (1-D)
photogate
flag
cart
air trough
velocity from flag length and gate time
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Momentum of the System
The momentum of the system is the sum (vector) of
the momenta.
The change in momentum of the system is the sum
(vector) of the changes in momenta.
The FBD of the system looks like...
And the net force is zero!!!
r
The momentum of the system does not change and
the initial momentum equals the final momentum,
for the system.
10
Two cars collides with a parked truck on glare
ice, (frictionless).
v 0
v
v, same as A
A
B
C
After A and B collide, C collides with B and B
comes to rest again.
mA m
mB 6m
mC m
before
After A and B collide, A is moving left at 1/2v
What happens to B?
Could we use 2nd law? Energy? Momentum?
NB,A
NA,B
3rd law pairs
11
Two cars collides with a parked truck on glare
ice, (frictionless).
v 0
before
v
v, same as A
After A and B collide, C collides with B and B
comes to rest again.
A
B
C
mA m
mB 6m
mC m
What happens to B?
after
vf,B ?
After A and B collide, A is moving left at 1/2v
v, same as A
v/2
A
B
C
mA m
mB 6m
mC m
Same, but opposite
Same for each, but opposite direction
Same for each block
During collision
A
B
3/2pA,i 3/2mv
3/2pA,i 3/2mv
Direction?
3rd law pairs
vf,B 1/4v
6mvf,B 3/2mvf,B
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Two cars collides with a parked truck on glare
ice, (frictionless).
after AB, before BC
1/4v
v, same as A
v/2
After A and B collide, C collides with B and B
comes to rest again.
A
B
C
mB 6m
mC m
mA m
What happens to C?
3/2pA,i 3/2mv left
1/2mv right
13
Two cars collides with a parked truck on glare
ice, (frictionless).
v 0
before
v
v, same as A
A
B
C
After A and B collide, C collides with B and B
comes to rest again.
mA m
mB 6m
mC m
after AB, before BC
v
v/2
v, same as A
What happens to C?
A
B
C
mB 6m
mC m
mA m
after BC collision
v 0
Summary
vf,C v/2
v/2
A
B
C
Momentum
mA m
mB 6m
mC m
A
B
C
B
initial
change
final
14
Two cars collides with a parked truck on glare
ice, (frictionless).
v 0
before
v
v, same as A
A
B
C
After A and B collide, C collides with B and B
comes to rest again.
mA m
mB 6m
mC m
after AB, before BC
v
v/2
v, same as A
What happens to C?
A
B
C
mB 6m
mC m
mA m
after BC collision
v 0
Summary
vf,C v/2
v/2
A
B
C
Momentum
mA m
mB 6m
mC m
Take a look a the initial and final momenta of
the system. They are both zero.
In facy, the momentum of the system is zreo
throughout!