Physics NYA – Mechanics
Dawson College
Lab #4 – Collisions in Two Dimensions
Introduction:
Purpose
The purpose of this experiment is to:
•
Verify the conservation of linear momentum by observing the collision of two pucks on a
flat air table.
•
Verify that the centre of mass of such a system has a velocity that is unchanged by the
collision.
In addition, you will:
•
Prepare an abbreviated report that contains only data, analysis and conclusions. It is not
necessary for this report to include an Introduction or Procedure section. One third of the
marks for your report will be based on your conclusion.
Theory
A - Conservation of Momentum
An alternate way of expressing Newton’s 2
nd
Law is with the linear momentum (
v
p
). Linear
momentum is defined in terms of the mass (m) and velocity (
v
v
) as:
v
v
p
mv
=
(1)
Newton’s 2
nd
Law can be written in terms of linear momentum as:
dt
p
d
F
ext
v
v
=
∑
where
∑
ext
F
v
is the sum of external forces acting on the mass.
If the sum of all external forces is zero
, then the time rate of change of linear momentum is
also zero – that is,
linear momentum doesn’t change
. If we therefore define two particles about
to collide as a single system, and if there are no other horizontal forces acting on this system
(like friction) then the total momentum before and after the collision will be the same:
0
=
−
=
Δ
∑
∑
before
after
p
p
p
v
v
r
(2)
If the pucks are labelled so that L=light, H=heavy, a=after and b=before, the x and y-directions
momentum conservation equations can be written as:
x-direction
:
( )( )
0
,
,
,
,
,
,
,
,
,
,
=
+
−
+
=
−
∑
∑
a
H
x
b
L
x
a
H
x
a
L
x
b
x
a
x
p
p
p
p
p
p
and
y-direction
:
0
,
,
,
,
,
,
,
,
,
,
=
+
−
+
=
−
∑
∑
a
H
y
b
L
y
a
H
y
a
L
y
b
y
a
y
p
p
p
p
p
p
B – Centre of mass and momentum
It is possible to identify the centre of mass (CM) of a two particle system – the point at which
the two masses would balance were they attached by a rigid massless rod. The distance (d
CM
) of
the centre of mass
from the lighter of the two masses along a line connecting them
is given in
terms of the total distance between the masses (D) and their masses as:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
=
L
H
H
CM
M
M
M
D
d
(3)