Investigation 13C: Center of mass

Essential questionsHow do we find the center of mass of an object?
What is the physics behind the balance beam event in gymnastics? Gymnasts must keep their center of gravity directly above the balance beam—or else they fall off! Every object (including a gymnast) has a center of gravity, which is the average position for all the mass in an object. In this investigation, you will find the center of mass of an irregularly shaped piece of cardboard. Once you find it, can you balance the cardboard on the tip of a pencil?
Part 1: Find the center of mass by hanging

Finding the center of mass of an object by hanging it from three holes
  1. Cut out an irregularly shaped piece of cardboard and use a pen or other sharp object to create three widely spaced holes near the edges of the cardboard.
  2. Using string, hang the object using one hole, trace the line of the string, and use a ruler to extend the line across the object.
  3. Repeat for the other two holes. Locate the center of mass at the intersection of the lines.
  1. Why does drawing a line below the hole pass through the center of mass?
  2. Why is the intersection of the three lines the center of mass?
  3. Try to balance the cardboard on the tip of a pencil. Where must you place the pencil?
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Part 2: Find the center of mass using a plumb line

Find the center of mass using a plumb line
  1. Insert a pencil through one hole to hang the object.
  2. Using string, hang a plumb line from the pencil and trace the path of the string on the cardboard.
  3. Repeat for the other two holes. Locate the center of mass at the intersection of the lines.
  1. Did you get the same center of mass as in Part 1?
  2. What happens to a gymnast when her center of mass is not located directly above her feet? Use the equipment to demonstrate what happens.
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