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Center of Mass & Simple Balance quiz #1

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  • What is the term for the point where the mass of a vehicle (or any object) is considered to be concentrated and balanced?
    The point where the mass of an object is concentrated and balanced is called the center of mass (or center of gravity).
  • Where is the center of mass located in a two-body system such as the Earth-Moon system?
    In a two-body system like the Earth-Moon system, the center of mass is located along the line connecting the two bodies, closer to the more massive object (Earth), and its position can be calculated using (m1*x1 + m2*x2) / (m1 + m2), where m and x are the masses and positions of the bodies.
  • For two objects orbiting each other, where is their center of mass located?
    The center of mass of two objects orbiting each other is always located along the line joining them, at a point determined by their masses and positions, given by (m1*x1 + m2*x2) / (m1 + m2).
  • How is the center of gravity of a body defined in physics?
    The center of gravity of a body is defined as the point where the entire weight of the body acts and where the mass is considered to be concentrated for the purpose of analyzing balance and equilibrium.
  • Where is the center of gravity located in a broom with non-uniform mass distribution, such as the one held up by Dr. Hewitt?
    For a broom with non-uniform mass distribution, the center of gravity is located closer to the heavier end, not at the geometric center.
  • What is a helpful method for locating the center of gravity of an object?
    A helpful method for locating the center of gravity of an object is to balance the object on a narrow edge or point; the location where it balances horizontally is its center of gravity.
  • Where is the center of gravity of a basketball located?
    The center of gravity of a basketball is located at its geometric center, assuming the mass is uniformly distributed.
  • Why does the famous Leaning Tower of Pisa not topple over?
    The Leaning Tower of Pisa does not topple over because its center of gravity remains above its base of support, maintaining equilibrium.
  • What happens to an object if its center of mass moves beyond the edge of its supporting surface?
    If the center of mass moves beyond the edge of the support, the object will tilt and lose equilibrium. This is because the weight force creates a torque that causes rotation about the support edge.
  • In a non-uniform mass distribution problem involving a person on a massless board with two scales, what does a higher reading on one scale indicate about the person's center of mass?
    A higher reading on one scale indicates that the person's center of mass is closer to that end of the board. This is because more weight is distributed toward the side with the greater normal force.
  • How does the position of the center of gravity affect the stability of an object?
    The position of the center of gravity is crucial for an object's stability. If the center of gravity is located within the support base, the object will remain balanced and in equilibrium. If the center of gravity extends beyond the support edge, the object will tilt and lose stability.