PASCO ME-6825A MINI LAUNCHER - Manual (Page 29)

012-05479B Mini Launcher
27
®
q
1
v
1
m
1
q
2
v
2
m
2
v
0
m
1
m
2
(u = 0)
Experiment 6: Conservation of Momentum In Two Dimensions
EQUIPMENT NEEDED
– Mini Launcher, 2 steel balls and Collision Attachment – Plumb bob
– Meter stick – Protractor
– Butcher paper – Tape to make collision inelastic
– Stand to hold ball – Carbon paper
Purpose
The purpose of this experiment is to show that the momentum is conserved in two dimensions for elastic
and inelastic collisions.
Theory
A ball is shot toward another ball which is
initially at rest. After the resulting collision
the two balls go off in different directions.
Both balls are falling under the influence of
the force of gravity so momentum is not
conserved in the vertical direction. How-
ever, there is no net force on the balls in the
horizontal plane so momentum is con-
served in horizontal plane.
Before the collision, since all the momen-
tum is in the direction of the velocity of
Ball #1, it is convenient to define the x-axis
along this direction. Then the momentum
before the collision is
P
before
= m
1
v
0
x
and the momentum after the collision is
P
after
= m
1
v
1x
+ m
2
v
2x
x + m
1
v
1y
- m
2
v
2y
y
where v
1x
= v
1
cos
θ
1
, v
1y
= v
1
sin
θ
1
, v
2x
= v
2
cos
θ
2
and v
2y
= v
2
sin
2
Since there is no net momentum in the y-direction before the collision, conservation of momentum
requires that there is no momentum in the y-direction after the collision.
Therefore,
m
1
v
1y
= m
2
v
2y
Equating the momentum in the x-direction before the collision to the momentum in the x-direction after
the collision gives
m
1
v
0
= m
1
v
1x
+ m
2
v
2x
In an elastic collision, energy is conserved as well as momentum.
1
2
m
1
v
0
2 = 1
2
m
1
v
1
2 + 1
2
m
2
v
2
2
Also, when energy is conserved, the paths of two balls (of equal mass) after the collision will be at right
angles to each other.
(a)
(b)
Figure 6.1: (a) Before Collision (b) After Collision