Announcements

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Announcements

• Homework for tomorrow
• (Ch. 8, Probs 2, 6, 8)
• Office hours
• MF 4-5 pm
• TR 11-12 pm, W 2-3 pm
• Tutorial Learning Center
• M 8-12 pm, 2 - 5 pm
• TW 8 am 7 pm
• R 8 am 4 pm, 5 7 pm
• F 8 9 am, 10 12 pm, 2 5 pm

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Chapter 8

• Extended Systems
• (Center of Mass)

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Quiz Question 1

• Suppose the entire population of the world
  gathers in one spot and, at the sounding of a
  prearranged signal, everyone jumps up.
• While all the people are in the air, does Earth
  gain momentum in the opposite direction?
• No the inertial mass of Earth is so large that
  the planets change in motion is imperceptible
• Yes because of its much larger inertial mass,
  however, the change in momentum of the Earth is
  much less than that of all the jumping people
• Yes Earth recoils, like a rifle firing a bullet,
  with a change in momentum equal to and opposite
  that of the people.
• It depends.

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Quiz Question 2

• Suppose the entire population of the world
  gathers in one spot and, at the sounding of a
  prearranged signal, everyone jumps up. About a
  second later, 6 billion people land back on the
  ground.
• After the people have landed, Earths momentum
  is
• the same as what it was before the people jumped.
• different from what it was before the people
  jumped.

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Section 8.1The Motion of Complex Objects

• Consider the diver pictured below
• We cannot simply treat the diver as a
  tossed particle.
• We must consider her as a system of particles

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Section 8.2 Defining the Position of a Complex
Object

• Consider two particles pictured below
• Q What is the net force acting on the system?
• What is the acceleration of the system?

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Defining the Position of a Complex Object
continued

• Q What is the effective position of the
  system?
• For 2 particles
• For N particles

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Center of Mass

• The effective position of a system is the center
  of mass of the system
• The center of mass of a body or a system of
  bodies is its balancing point.
• It is the point that moves as though all of the
  mass were concentrated there and the system
  behaves as if all the external forces are applied
  there.

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Things to know about Center of Mass

• Sometimes easy to find from symmetry
• For all practical purposes
• C of M C of G
• Gravity acts on the body as if mass is
  concentrated at
  the C of M
• Free bodies like to rotate about the C of M

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Section 8.4 Locating a Systems Center of Mass

• The components of the center of mass of a system
  of particles are

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Touchstone Example 8.1

• Three particles of masses mA 1.2 kg, mB 2.5
  kg, and mC 3.4 kg form an equilateral triangle
  of edge length a 140 cm.
• Where is the center of mass of this
  three-particle system?

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Touchstone Example 8.2

• The U-shaped object has outside dimensions of 100
  mm on each side, and each of its sides is 20 mm
  wide. It was cut from a uniform sheet of plastic
  6.0 mm thick.
• Locate the center of mass of this object.