Homework 7 Due February 27 2007
 1 
1) The velocity of the center of mass for a system of particles is defined to be
total
cm
total
p
v
m
=
G
G
where
p
total
is the total momentum of the system and
m
total
is the total mass of the system.
Consider a system of two particles that undergo an elastic collision in 1dimension
.
Particle A has mass
m
A
, initial velocity
v
A
1
and final velocity
v
A
2
. Particle B has mass
m
B
,
initial velocity
v
B
1
and final velocity
v
B
2
.
a) Which conservation implies that the center of mass velocity of the system does not
change during the collision? Show that:
1
1
2
2
A
A
B
B
A
A
B
B
cm
A
B
A
B
m v
m v
m v
m v
v
m
m
m
m
+
+
=
=
+
+
b) We will consider the motion of these particles in two frames of reference, the "lab"
frame which is stationary and the “center of mass” frame which is moving at
v
cm
. What is
the relation between
v
A
1
/lab
and
v
A
1
/cm
;
v
A
2
/lab
and
v
A
2
/cm
;
v
B
1
/lab
and
v
B
1
/cm
;
v
B
2
/lab
and v
B
2
/cm
v
cm/lab
and v
cm/cm
.
c) Using conservation of momentum and energy in the center of mass frame, show that in
an elastic collision, the center of mass velocities satisfy:
2/cm
1/cm
2/cm
1/cm
A
A
B
B
v
v
v
v
= −
= −
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 Spring '08
 HerreraSiklody
 Center Of Mass, Mass, Momentum, Work

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