PH1004
Exp 3: Collisions
1
PH 1004 Laboratory Instructions
Experiment 3
Collisions
Backgr
o
und
A collision is an isolated event in which each colliding particle exerts a force on
one or more other particles for a relatively short period of time.
Collisions can take place
in many different forms and intensities.
One example is a baseball bat coming into
contact with a baseball.
Another is a meteor striking a planet.
In general, collisions can be categorized as elastic, inelastic, and perfectly
inelastic.
For an elastic collision, the momentum and the kinetic energy are both
conserved.
For an inelastic collision, only the momentum is conserved.
A perfectly
inelastic collision is one in which the colliding bodies or particles stick together after the
collision.
The example above of the meteor striking the planet is one such type of
collision.
In this experiment, we will use an air track to investigate the conservation of
momentum and kinetic energy for elastic collisions, and the conservation of momentum
for perfectly inelastic collisions.
Collisions are characterized by momentum and impulse. To understand the
concepts of momentum and impulse, we have to understand how these relate to physical
concepts which we already know, such as forces and velocities.
The
momentum
of an
object is a vector quantity with the magnitude of mass times velocity:
v
m
p
r
r
=
(31)
The direction of the momentum vector coincides with that of the velocity vector. If we
differentiate the momentum with respect to the time, we obtain:
a
m
dt
v
d
m
v
m
dt
d
dt
p
d
r
r
r
r
=
=
=
)
(
.
(32)
Recalling Newton’s second law,
a
m
F
r
r
=
, we can write
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PH1004
Exp 3: Collisions
2
dt
p
d
F
r
r
=
.
(33)
Now consider a system of many objects, or particles, each with its own mass,
velocity and momentum. The system of particles as a whole has a total linear
momentum,
P
r
, which is defined as the vector sum of the individual momenta:
3
2
1
...
p
p
p
P
r
r
r
r
+
+
+
=
(34)
In terms of the velocity of the center of mass,
com
v
r
:
com
v
M
P
r
r
=
(35)
where
M
=
m
1
+
m
2
+…+
m
n
is the total mass of the system. Taking the time derivative of
Equation 35, we find
com
com
a
M
dt
v
d
M
dt
P
d
r
r
r
=
=
.
(36)
Now, similarly to Equation (33), we may write Newton’s second Law for the system of
colliding particles in the form
dt
P
d
F
net
r
r
=
.
(37)
where
net
F
r
is the net external force acting on the system.
Consider now a typical collision between two objects.
Because the collision time
is short and the forces between the particles in collision are large, it is generally a good
approximation to assume that there are no significant external forces acting on the two
object system during the collision.
Setting
0
=
net
F
r
in Equation 37 then yields
0
=
dt
P
d
r
and
P
r
= constant. Thus, the momentum of the system is conserved.
In other words, for
both elastic and inelastic collisions, the vector sum of the momentum for each colliding
object before the collision is equal to the vector sum of the momentum after the collision.
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 Spring '08
 WORMER
 Physics, Force, Kinetic Energy, Momentum, Collision, glider, kinetic energies

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