PASCO ME-6800 Projectile Launcher (Short Range) - Manual (Page 31)

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M o d e l N o . M E - 6 8 0 0 E x p . 6 : C o n s e r v a t i o n o f M o m e n t u m
0 1 2 - 0 5 0 4 3 G 27
Exp. 6: Conservation of Momentum
Equipment Needed
Purpose
The purpose of this experiment is to confirm that momentum is conserved for elastic and inelastic collisions in two
dimensions.
Theory
A ball is shot toward another ball that is initially at rest,
resulting in a collision after which the two balls move in
different directions. In the system consisting of just the
balls, both balls are falling under the influence of gravity
so momentum is not conserved in the vertical direction.
However, there is no net force in the horizontal plane (if
air resistance is ignored), so momentum is conserved in
the horizontal plane.
Before collision, since all the momentum is in the direc-
tion of Ball #1 (m
1
), it is convenient to define the x-axis in
this direction. Momentum before the collision is:
where v
0
is the initial speed of Ball #1 and is the unit vector in the x-direction. The momenta of the two balls
after the collision consists of both horizontal and vertical components, so the momentum after the collision is:
where v
1x
= v
1
cos

1
, v
1y
= v
1
sin

1
. v
2x
= v
2
cos

2
, and v
2y
= v
2
sin

2
.
Since there is no momentum in the y-direction before the collision, there is zero net momentum in the y-direction
after the collision. Therefore, t
Equating the momentum in the x-direction before the collision to the momentum in the x-direction after the colli-
sion gives:
In a perfectly elastic collision, kinetic energy is conserved as well as momentum.
Also, when energy is conserved, the paths of two balls of equal mass will be at right angles to each other after the
collision.
Item Item
Projectile Launcher and 2 plastic balls 2-D Collision Accessory
Meter stick or measuring tape Sticky tape
White paper, large sheet Carbon paper (2 or 3 sheets)
Protractor Plumb bob and string
υ
0
m
1
m
2
(
υ = 0)
(a)
θ
1
υ
1
m
1
θ
2
υ
2
m
2
(b)
Figure 6.1: Conservation of Momentum
(a) before collision (b) after collision
P
before
m
1
v
0
xˆ =
xˆ
P
after
m
1
v
1x
m
2
v
2x
+
 xˆ
m
1
v
1y
m
2
v
2y
+
 yˆ
+ =
m
1
v
1y
m
2
v
2y
– =
m
1
v
0
m
1
v
1x
m
2
v
2x
+ =
1
2
---m
1
v
0
2 1
2
---m
1
v
1
2 1
2
---m
2
v
2
2
+ =