http://www.ck12.org Chapter 7. Momentum
7.3 Conservation of Momentum and Center of Mass
Objectives
The student will:
- Understand conservation of momentum
- Be able to solve problems using the conservation of momentum
- Understand the motion of the center of mass of a system
Vocabulary
- Center of mass: The balancing point of a system, or the point at which all of the mass in a system is
concentrated. - Conservation of Momentum:The change in the total momentum of a system is zero.
Introduction
A conservation principle states that there is a quantity which remains constant within a system. Earlier, we concen-
trated on the conservation of mechanical energy. We now consider the conservation of momentum by once again
referring back to Newton’s Second Law (N2L). As a reminder, N2L states that a net force on a massmwill accelerate
the massm, that is∑F=Fnet=ma.
When we discussed impulses, we rewrote N2L asF=mvf∆−tmvi→F∆t=mvf−mvi=∆p. Recall thatFrepresents
the net force on the object (or system) in question. The equation states that if the net force on the system is zero,
the change in momentum of the system must also be zero since 0=mvf∆−tmvi=∆p→∆p=mvf−mvi=0. We can
write this result as a conservation principle by stating∆p=pf−pi= 0 →pi=pf. We claim that it represents a
conservation principle because we’re led to a similar conclusion as we saw with the conservation of energy. The
initial energy of the system equaled the final energy of the system(Ei=Ef). Here, we have been lead to the
conclusion that the initial momentum of the system equals the final momentum of the system(pi=pf).
In general, for any isolated system, the change in the total momentum of the system is zero. As long as this condition
holds, the momentum of a system with any number of interacting objects is conserved.
Illustrative Example 7.3.1
This is a very familiar example of momentum conservation. You may have seen this using a “Newton’s Cradle”
apparatus (Figure7.9), but the same conservation principle can be easily demonstrated using two identical marbles
or two identical coins.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/112394