Mature animals are not just bigger versions of juvenile animals, they also have a different shape. In this activity we will use clay sculptures to explore some of the reasons behind this fact.

Each person should obtain a piece of clay about the size of a large fist.

1. Form a small piece of clay into a spherical ball about 2 to 3 cm in diameter and record the exact diameter and weight in your lab notebook.
2. Next make a spherical ball which is roughly twice the diameter you chose for the first ball and record its exact diameter and weight in your lab notebook.

By what factor is the second ball larger in diameter than the first ball?

By what factor is the second ball larger in mass than the first ball?

Explain, mathematically, what you observe.

 

 

3. Next try estimate the diameter of a ball of clay which will weigh twice as much as the first ball. Use as much clay as you need to make a ball with this diameter. Record its diameter and weight in you lab notebook. Did you make an accurate guess?

Save your data. In the computer lab you will plot this data to find a graphical representation of the relationship between mass and size of geometrically similar objects.

1. Make a small person out of clay about 3 cm tall. Make a geometrically similar larger person out of clay about 15 cm tall. Try making them both stand up.

Which figure has better posture? Why?

 

Now modify the form of the taller person so that it has better posture (Does making the person skinnier or wider help?, what about adding legs?)

2. To investigate how form affects stability in a more quantitative way we will now restrict our attention to cylindrical figures. Make several cylinders with different diameters but all about 3 cm tall.

For cylinders of this height find the smallest diameter you can make so that the cylinder doesn’t sag when place on its flat end. (make sure you keep the shape cylindrical). Find the ratio of height to diameter. Record the diameter, height and mass in your notebook.

 

3. Now make a cylinder about 15 cm tall with as small a diameter as possible so that it doesn’t sag when placed on end.. Find the ratio of height to diameter. Is this ratio the same as in the case of the first cylinder? Record the diameter, height and mass in your notebook.

 

4. Take all your clay and make a cylinder which is as tall as possible without sagging. Find the ratio of height to diameter. Has this quantity changed? Record the diameter, height and mass in your notebook..

 

We will collect all this data together in the computer lab and determine how height and mass depend on diameter when shape is allowed to change.

5. Finally, choosing any shape you want make the tallest sculpture you can with all your clay. Comment on how the shape you have made helps support the sculpture.