Page 128 - Fisika Terapan for Engineers and Scientists

328 CHAPTER 10 Systems of Particles

kinetic energy [Eq. (10.42)] and the total potential energy. This total energy will be
conserved during the motion of the system of particles. Note that in reckoning the
total potential energy of the system, we must include the potential energy of both the
external forces and the internal forces. We know that the internal forces do not con-
tribute to the changes of total momentum of the system, but these internal forces, and
their potential energies, contribute to the total energy. For instance, if two particles
are falling toward each other under the influence of their mutual gravitational attrac-
tion, the momentum gained by one particle is balanced by momentum lost by the
other, but the kinetic energy gained by one particle is not balanced by kinetic energy
lost by the other—both particles gain kinetic energy. In this example the gravitational
attraction plays the role of an internal force in the system, and the gain of kinetic energy
is due to a loss of mutual gravitational potential energy.

✔ Checkup 10.4

QUESTION 1: Consider a system consisting of two automobiles of equal mass. Initially,
the automobiles have velocities of equal magnitudes in opposite directions. Suppose the
automobiles collide head-on. Is the kinetic energy conserved?
QUESTION 2: The Solar System consists of the Sun, nine planets, and their moons. Is
the total energy of this system conserved? Is the kinetic energy conserved? Is the poten-
tial energy conserved?
QUESTION 3: Two equal masses on a frictionless horizontal surface are connected by
a spring. Each is given a brief push in a different direction. During the subsequent
motion, which of the following remain(s) constant? (P total momentum; K total
kinetic energy; U total potential energy.)
(A) P only (B) P and K (C) P and U
(D) K and U (E) P, K, and U

SUMMARY

PROBLEM-SOLVING TECHNIQUES Conservation of Momentum (page 310)

PROBLEM-SOLVING TECHNIQUES Center of Mass (page 320)

PHYSICS IN PRACTICE Center of Mass and Stability (page 320)

MOMENTUM OF A PARTICLE p mv (10.1)

MOMENTUM OF A SYSTEM OF PARTICLES P p p p (10.4)
1 2 n

RATE OF CHANGE OF MOMENTUM dP
F (10.13)
dt ext
CONSERVATION OF MOMENTUM P [constant] (10.12)
(in the absence of external forces)