Chapter-9 Center of Mass and Linear Momentum

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Chapter-9Center of Mass and Linear
Momentum    
In this chapter we will introduce the following
new concepts -Center of mass (com) for a system
of particles-The velocity and acceleration of
the center of mass -Linear momentum for a single
particle and a system of particles We will
derive the equation of motion for the center of
mass, and discuss the principle of conservation
of linear momentum.
Finally, we will use the
conservation of linear momentum to study
collisions in one and two dimensions and derive
the equation of motion for rockets.
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Why study Center of Mass?
(a) A ball tossed into the air follows a
parabolic path. (b) The center of mass (black
dot) of a baseball bat flipped into the air
follows a parabolic path, but all other points of
the bat follow more complicated curved paths.
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9.2   The Center of Mass
The center of mass of a system of particles is
the point that moves as though (1) all of the
systems mass were concentrated there and (2)
all external forces were applied there.
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Center of Mass of Systems of Particles
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Problem 4
4   In Fig. 9-37, three uniform thin rods, each
of length L 22 cm, form an inverted U. The
vertical rods each have a mass of 14 g the
horizontal rod has a mass of 42 g. What are (a)
the x coordinate and (b) the y coordinate of the
system's center of mass?
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9.3   Newton's Second Law for a System of
Particles
9-14

• Fnet is the net force of all external
  forces that act on the system. Forces on one part
  of the system from another part of the system
  (internal forces) are not included in Eq. 9-14.
• M is the total mass of the system. We assume
  that no mass enters or leaves the system as it
  moves, so that M remains constant. The system is
  said to be closed.
• a com is the acceleration of the center
  of mass of the system. Equation 9-14 gives no
  information about the acceleration of any other
  point of the system.
• Proof of Equation 9-14
• Q 1 Figure 9-23 shows an overhead view of three
  particles on which external forces act. The
  magnitudes and directions of the forces on two of
  the particles are indicated. What are the
  magnitude and direction of the force acting on
  the third particle if the center of mass of the
  three-particle system is (a) stationary, (b)
  moving at a constant velocity rightward, and (c)
  accelerating rightward?