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Lecture 12
Collisions in One and Two Dimensions
Center of Mass
Physics 111, Summer 2011, July 5, Lecture 12
Summary
Linear momentum is the product of the
r
r
A quantity called “linear momentum” incorporates the ideas of mass and
velocity similar to kinetic energy but the linear momentum is a vector quantity.
mass
and the velocity
of any moving object:
Second Newton’s Law in
terms of linear momentum:
v
m
p
t
p
t
v
m
t
v
m
a
m
F
Δ
Δ
=
Δ
Δ
=
Δ
Δ
=
=
∑
r
r
r
r
r
)
(
If the total external force
acting on the system is
zero, the total momentum
of the system is conserved:
const
p
p
p
B
A
total
=
+
=
2
Force acting on an object during any collision:
Impulse (change in linear momentum = force x time):
t
F
p
Δ
=
Δ
∑
r
r
t
p
F
Δ
Δ
=
∑
r
r
Physics 111, Summer 2011, July 5, Lecture 12
Collisions
Collision
:
any strong interaction during relatively short time between moving
relatively each other objects.
♦
There are two major parameters, which can be discussed for any collision:
Types of collisions:
1. Linear momentum.
2. Kinetic energy.
Elastic collision
: The total kinetic energy
of the system is the same after the
collision as before.
3
Inelastic collision
: The total kinetic energy
of the system after the collision is
less than before.
The linear momentum
of the system always is conserved (is the same after
the collision as before).
Physics 111, Summer 2011, July 5, Lecture 12
Elastic Collision
Linear momentum
and kinetic energy
of the system are conserved
:
after the collision they are the same as those before.
After the collision, two objects move separately
.
fin
B
B
fin
A
A
init
B
B
init
A
A
fin
init
v
m
v
m
v
m
v
m
or
p
p
)
(
)
(
)
(
)
(
+
=
+
=
inetic energy before and after collision:
Linear momentum of two objects before and after collision:
4
fin
B
B
fin
A
A
init
B
B
init
A
A
fin
init
v
m
v
m
v
m
v
m
or
KE
KE
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
2
2
2
2
2
2
2
2
Kinetic energy before and after collision:
Physics 111, Summer 2011, July 5, Lecture 12

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Elastic Collision (#1)
A 1000 kg car moves at 3 m/s and hits a stationary 2000 kg truck. After

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