Totally elastic collisions
•
To calculate the result of an elastic collision in one dimension, we considered
e constraints of total momentum and energy conservation:
the constraints of total momentum and energy conservation:
f
f
tot
v
m
v
m
v
m
v
m
p
,
2
2
,
1
1
0
,
2
2
0
,
1
1
:
1
Eq.
+
=
+
=
2
1
2
1
2
1
2
1
q
,
2
2
2
,
1
1
2
0
,
2
2
2
0
,
1
1
2
:
2
Eq.
f
f
tot
v
m
v
m
v
m
v
m
E
+
=
+
=
•
We rearrange both equations to get object 1 on the left and object 2 on the
right:
q
earranged
−
=
−
( ) ( )
0
,
2
,
2
2
,
1
0
,
1
1
:
1
Eq.
Rearranged
v
v
m
v
v
m
f
f
()
2
0
,
2
2
,
2
2
2
1
2
,
1
2
0
,
1
1
2
1
:
2
Eq.
Rearranged
v
v
m
v
v
m
f
f
−
=
−
−
=
−
( )( ) ( )( )
0
,
2
,
2
0
,
2
,
2
2
,
1
0
,
1
,
1
0
,
1
1
v
v
v
v
m
v
v
v
v
m
f
f
f
f
+
+
(
)
0
,
2
,
2
,
1
0
,
1
:
2
New Eq.
v
v
v
v
f
f
+
=
+
•
Combining the last equation and the rearranged Equation 1, we have two
equations and 2 unknowns which we can solve to get
v
1,f
and
v
2,f
:
0
,
2
2
1
2
0
,
1
2
1
2
1
,
1
2
v
m
m
m
v
m
m
m
m
v
f
+
+
+
−
=
0
,
1
2
1
1
0
,
2
2
1
1
2
,
2
2
v
m
m
m
v
m
m
m
m
v
f
+
+
+
−
=