Chapter 9a Systems of Particles

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Chapter 9a - Systems of Particles

• Center of Mass
• point masses
• solid objects
• Newtons Second Law for a System of Particles
• Linear Momentum for a System of Particles
• Conservation of Linear Momentum
• Rockets
• Internal Energy/External Forces

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Calculating the center of mass point objects
1 D
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Calculating the center of mass point objects
2 D
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Problem 1

• Three masses located in the x-y plane have the
  following coordinates
• 2 kg at (3,-2)
• 3 kg at (-2,4)
• 1 kg at (2,2)
• Find the location of the center of mass

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Calculating the center of mass solid objects
1 D
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Calculating the center of mass solid objects
2 D
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Finding the COM
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Problem 2

• What is the center of mass of the Letter F
  shown if it has uniform density and thickness?

2cm
2cm
20cm
5cm
10 cm
2cm
15cm
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Problem 3
The blue disk has a radius 2R The white area is
a hole in the Disk with radius R. Where is the
center of mass?
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COM and translational motion
First time derivative
COM Momentum
Second time derivative
Newtons 2nd Law
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What this means.

• The sum of all forces acting on the system is
  equal to the total mass of the system times the
  acceleration of the center of mass.
• The center of mass of a system of particles with
  total mass M moves like a single particle of mass
  M acted upon by the same net external force.

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Conservation of Linear Momentum

• If 2 (or more) particles of masses m1, m2,
  form an isolated system (zero net external
  force), then total momentum of the system is
  conserved regardless of the nature of the force
  between them.

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Problem 1

• An astronaut finds himself at rest in space after
  breaking his lifeline. With only a space tool in
  his hand, how can he get back to his ship which
  is only 10 m away and out of his reach.

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Variable mass Rocket propulsion
small
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Rocket thrust
Find Thrust, initial net force, net force as
all fuel expended