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Finding the Centre of Gravity

Finding the centre of gravity of an irregularly-shaped object is trickier than for a ruler or other regular shape. In this activity, students use the force of gravity to deduce the centre of gravity for various shapes.

Since the weight of an object is concentrated in its centre of gravity, the force of gravity passes through this point in a vertical line towards the Earth. An object hanging from any point will automatically rotate so that its centre of gravity is along this vertical line from the hanging point.

In this activity, a plumb line (a weighted string) is created in order to visualize the vertical gravitational pull towards the Earth. Hanging the shape at any point will cause the shape to rotate until its centre of gravity lines up directly below the hanging point.

Drawing a line along the plumb line enables us to see the vertical line between the hanging point and the centre of the earth. The problem is that one line is not sufficient to pinpoint the exact centre of gravity of the shape (it could be anywhere along this line). This is why we hang the shape at a different point and draw another line along the plumb line.

The intersection of the two plumb lines is the object's centre of gravity. When students hang the shape from several different points they see that the plumb line always passes through the same spot.

You have correctly marked the shape's centre of gravity if:

  • when you pin your shape through its centre of gravity it is stable and balanced.
  • you can balance the shape by placing your finger under the centre of gravity.

An object will topple over once its centre of gravity falls outside its base of support. To answer a brainteaser on whether or not an object will topple over, students can draw a plumb line between the object's centre of gravity and its base. If the plumb line falls outside of the base of support, the object will topple over. This is why the Leaning Tower of Pisa does not topple over: its centre of gravity is still above its base when a plumb line is drawn. If it were leaning more, it would topple over since the plumb line would fall outside the base.

Objectives

  • Examine the concept of the centre of gravity.

  • Use the force of gravity to deduce the centre of gravity for various shapes.

Materials

  • Per Group of 4 Students:
    4 cardstock shapes, either pre-cut or printed for students to cut out (see shape card templates)
    4 pairs of scissors
    a pin or tack
    a 20 cm piece of string
    a chalk or pen (colour should contrast the shapes’ colour)
    a small weight to hang from the string (e.g. washer, eraser, key)

Key Questions

  • Which force does the plumb line follow?
  • Why do we have to draw several lines from different points?
  • What does the spot where your lines intersect represent?
  • How can you check that you have correctly found your shape’s centre of gravity?
  • Is the centre of gravity exactly in the middle (geometric centre) of the shape?
  • What does it mean to say that something is “balanced”?

What To Do

Preparation:

Pre-cut templates or photocopy irregular shape templates onto cardstock.

Activity:

  1. Attach a small weight to the end of your string. This is your plumb line: it follows the direction of the gravitational pull.
  2. If using chalk, cover the string with chalk. If not, skip this step.
  3. Hang the plumb line on the pin. Pierce the pin anywhere along the edge of the shape, so that your shape is free to swing/rotate.
  4. Hold the pin and wait until the shape and the plumb line have settled. Mark where the string crosses the shape by “twanging” the string to leave a chalk mark, or trace the string’s path with a pen if you are not using chalk.
  5. Remove the pin and plumb line from the shape. Pierce them through another point along the shape’s edge. It shouldn’t be too close to the last hole you made.
  6. Repeat steps 1 to 6 three more times.
  7. Mark the spot where the lines intersect.
  8. Repeat with another shape.

Extensions

  • Use cardboard templates that are in the shape of the Provinces and Territories to find the centre of gravity for each.