Pasco Scientific ME-6825, Instruction Manual And Experiment Manual

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012-05479A Mini Launcher
27
θ
1
v
1
m
1
θ
2
v
2
m
2
v
0
m
1
m
2
( υ = 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. However,
there is no net force on the balls in the hori-
zontal plane so momentum is conserved in
horizontal plane.
Before the collision, since all the momentum
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
1 x
+ m
2
v
2 x
x + m
1
v
1 y
– m
2
v
2 y
y
where
v
1 x
= v
1
cos
θ
1
,
v
1 y
= v
1
sin
θ
1
,
v
2 x
= v
2
cos
θ
2
and
v
2 y
= v
2
sin
θ
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
1 y
= m
2
v
2 y
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
1 x
+ m
2
v
2 x
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