# Challenge Two

## Bone Geometry

### INTRODUCTION:

This experiment is designed to show one reason why human long bones are so strong.  Two parts of the long bone are the compact bone and spongy bone (cancellous bone). The compact bone is a cylinder.  The spongy bone is inside the compact bone and the spongy bone contains struts.  These struts form many triangles.  Let’s find out what the struts do for the bones!

### MATERIALS:

• 6 straws
• Ruler
• Scissors
• 4 small binder clamps

### WHAT TO DO:

You are going to construct some geometric shapes.  They behave differently when forces are exerted against them.  You are to determine which shape or structure is the strongest.

Cut 4 straws so they are 10 cm (4 inches) long.  Discard the small pieces.  Clamp the four pieces of straw together to make a square.  Measure the distance diagonally across the square and cut the remaining two straws slightly longer than that distance to give you straws of that longer length.  Discard the small pieces.

You will use these straws and clamps to make each structure listed in the chart on the next page.  Start with the 4 shorter pieces of straw.  After you have made a structure, you will draw it on the chart.  Then you will write on the chart the geometric shape(s) you see.  Look at your structure carefully.  Look for different geometric shapes.  Record the name of the shape(s) and the correct number of each shape in your structure.  Place the number in front of the name of the geometric shape.

Finally, write in the column on the right how strong you find the structure when you push its sides.  Hold the straw structure and move your hands slowly back and forth.  Do not bend the straws when you push them.  If any part of the straw bends, start again. Strength is determined by how much the structure can be pushed out of its original shape.  In answering this part of the lab report, compare one structure with another. Do not fill in the strength of a triangle section of the chart until you have tested the strength of a square.  Does the structure keep its shape or does it lose its shape?  How hard did you push to change its shape?

The ideas you learn in this laboratory exercise are related to the structure and strength of the bones of your body.  Your class can discuss this relationship at the conclusion of this work.

## BONE GEOMETRY

SHAPE (structure)

DRAWING

NAME AND NUMBER OF EACH GEOMETRIC SHAPE

STRENGTH:
MAKE COMPARISONS

SQUARE

TRIANGLE

SQUARE WITH ONE
CROSSBAR

SQUARE WITH TWO
CROSSBARS

1. Was the square or triangle stronger?

2. What happened to the strength of the square when you added crossbars?  Why?

3. If you were constructing a door with ten boards, how would you construct it?  Draw         your answer on the back of this paper or a separate paper.   Do not use ink.

### CHART:

Drawing:  Students will draw a square, triangle, a square with a crossbar, and a square with two crossbars.

Number of geometric shapes:

• square:  1 square

• triangle:  1 triangle

• square with 1 crossbar:  1 square; 2 triangles

• square with 2 crossbars: 1 square; 8 triangles

### QUESTIONS: ‌

1.  The triangle was stronger than the square.

2.  The square became stronger as crossbars were added because they formed additional triangles inside the square.  The triangle is the strongest geometric shape.

3.  There is no one correct answer to this question.  Each student may produce a different correct answer.   The door should include at least one crossbar going across all the other boards. It will create triangles.  Have students explain their solutions and perhaps display them in some manner.