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Chapter 6
Momentum and Collisions
Momentum
Defnition:
Important because it is CONSERVED
prooF:
Since ±
12
=±
21
,
For isolated particles never changes!
!
p
=
m
!
v
!
F
=
m
!
!
v
!
t
=
!
!
p
!
t
!
F
!
t
=
!
!
p
!
!
p
1
+
!
!
p
2
=
0
!
p
i
!
Vector quantity
•
Both
!
p
x
and
!
p
y
are conserved
p
x
=
mv
x
p
y
=
mv
y
Example 6.1
An astronaut of mass 80 kg
pushes away from a space
station by throwing a 0.75
kg wrench which moves with
a velocity of 24 m/s relative
to the original frame of the
astronaut. What is the
astronaut’s recoil speed?
0.225 m/s
Center of mass does not accelerate
X
cm
!
m
1
x
1
+
m
2
x
2
+
m
3
x
3
+
...
(
m
1
+
m
2
+
m
3
+
...)
!
X
cm
=
m
1
!
x
1
+
m
2
!
x
2
+
m
3
!
x
3
+
...
(
m
1
+
m
2
+
m
3
+
...)
=
!
t
"
m
1
(
!
x
1
/
!
t
)
+
m
2
(
!
x
2
/
!
t
)
+
m
3
(
!
x
3
/
!
t
)
+
...
(
m
1
+
m
2
+
m
3
+
...)
=
!
t
"
p
1
+
p
2
+
p
3
+
...
(
m
1
+
m
2
+
m
3
+
...)
=
0 if total
P
iszero
Do the backtoback demo
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View Full DocumentExample 6.2
Ted and his iceboat (combined mass = 240 kg) rest on the
frictionless surface of a frozen lake. A heavy rope (mass
of 80 kg and length of 100 m) is laid out in a line along
the top of the lake. Initially, Ted and the rope are at
rest. At time t=0, Ted turns on a winch which winds 0.5 m
of rope onto the boat every second.
a) What is Ted’s velocity just after the winch turns on?
b) What is the velocity of the rope at the same time?
c) What is the Ted’s speed just as the rope finishes?
d) How far did the centerofmass of Ted+boat+rope move
e) How far did Ted move?
f) How far did the centerofmass of the rope move?
0.125 m/s
0.375 m/s
0
0
12.5 m
37.5 m
Example 6.3
A 1967 Corvette of mass
1450 kg moving with a
velocity of 100 mph
(= 44.7 m/s) slides on a
slick street and collides
with a Hummer of mass
3250 kg which is parked
on the side of the street.
The two vehicles interlock
and slide off together.
What is the speed of the
two vehicles immediately
after they join?
13.8 m/s
=30.9 mph
Impulse
Useful for sudden changes when not interested in
force but only effects of force
Impulse
=
F
!
t
=
!
p
Bunjee Jumper Demo
Graphical Representation of Impulse
For complicated
force,
"
p is area
under F vs. t curve
F
t
Total Impulse
"
t
F
Impulse
=
F
!
t
=
!
p
Example 6.4
A pitcher throws a 0.145kg baseball
so that it crosses home plate
horizontally with a speed of 40 m/s.
It is hit straight back at the pitcher
with a final speed of 50 m/s.
a) What is the impulse delivered to
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 Spring '06
 Pratt
 Physics, Momentum

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