7.3. Conservation of Momentum and Center of Mass http://www.ck12.org
(1) If she takes the ground as her reference frame she now has a nonzero momentum. In fact, her momentum (along
with the remaining 9 baseballs and bag) has the same magnitude as the momentum of the first baseball that she
threw: 1. 015 kg∗sm
(2) Nothing prevents her from assuming that she is at rest with an initial momentum of zero and the ground is in
motion moving away from her with a speed of 3.22 cm/s.
1b. Is it as easy for the girl to throw the second ball with a velocity on 7.00 m/s due west relative to the ground as it
was for her to throw the first ball?
Answer:No, she must throw the baseball with a bit more force. Remember that she is moving 3.22 cm/s due west
and she throws the baseball due east. If she threw the baseball exactly as before, its velocity relative to the ground
would be a bit less:
- 00 ms− 0. 0322 ms= 6. 968 → 6. 97 ms
(3) The resulting velocity of the girl of Example 7.3.3 is quite small. However, should she keep throwing more
baseballs, her speed relative to the ground will keep increasing
Center of Mass
The fact that momentum is conserved only if the net force on the system is zero has a rather interesting implication.
Recall Newton’s First Law:
An object at rest stays at rest or an object in motion stays in the same state of motion, unless acted upon by an
unbalanced force, that is, a net force not equal to zero.
In other words, if the net force on the system is zero, the system must remain moving without change. At first glance
this appears a strange statement in light of what we’ve seen in these examples. After all, the motion of the objects
in the system clearly seemed to change in these situations. The car that was hit from behind in Example 6 certainly
did not remain at rest, and neither did the girl in Example 7. The key to understanding that everything remains in the
same state is to look at the system, not the parts of the system.
In order to analyze the motion of the system, we must focus our attention on thecenter of massof the system. It
turns out that it is the center of mass of the system that obeys Newton’s First Law.
The location of the center of mass of a system can be thought of as the balancing point of the system. For example,
if you place your figure at the 50-cm mark under a meter stick, the meter stick will balance on your finger. In effect,
it is the point at which all of the mass of the system is concentrated. Say, we have two identical 5-g marbles placed
16 cm apart from each other. If we imagine a fine wire rigidly connecting the two marbles, we could balance the
system by placing our finger at a distance of 8-cm from each marble. The 50-cm position of the meter stick and
the 8-cm position between the two marbles are the center of mass of each system. For the simple case of two-mass
systems where the masses are identical, the center of mass will always be at the geometric center of the system. If
the masses are not identical, finding the exact location of the center of mass becomes a bit more challenging and we
will not consider it here.
The Center of Mass and Newton’s First Law
Illustrative Example 7.3.5
InFigure7.13, blockAwith massmis moving with a velocity 10 m/s and blockBwith the same massmis at rest.
The two blocks are initially separated by a distance of 100 m. (a) Where is the center of mass(CM)of the two-block
system? (b) What is the velocity of the center of mass of the two-block system?
Answers:
a. Since both blocks have the same mass and are separated by a distance of 100-m, the center of the two-block