The Leaning Tower of Pisa seems to defy gravity. It is famous for its tilt of 14.5 feet (4.4 meters) when measured from the third floor. Its lean became obvious in 1178 at a height of 35 feet (10.6 meters) during construction of its third story. Two reasons are given for its lean - its being being built upon marshy, sandy soil and the tower's causing the ground upon which it is built to sink.

Many attempts, some successful and some not successful, have been made this century to stop the progression of the tilt of the tower. Cement was injected into its base in 1934. This accelerated its lean. Lead was added on its north side in 1994, causing it to tilt 2.5 mm overnight. Since 1994, more lead has been added, straightening the tower's lean about one centimeter.

Why do you think engineers throughout this century have tried to correct its tilt by adding mass to its base?

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Objective

• Students will construct a "tower" as high as possible that can successfully lean without collapsing.
• Students will examine the effect that lowering an object's center of gravity has on the torque produced on an object.

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Materials

• a box of 100 drinking straws
• modeling clay
• board or shelving
• protractor

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Design Requirements

• The tower must be constructed so that it can be transferred to a piece of wood shelving or board after finishing.
• Structures that look like "pallisades" are not allowed. Only "tinker toy" structures are allowed.
• Each structure must use a minimum of 15 straws.
• The structure must be built perpendicular to its base. In other words, it cannot be built with a "lean."
• You cannot cut the straws.
• Straws can only be connected using clay.
• During testing, a tower cannot lean more than 10 °.

Procedure

1. You will be given the first half of the class in which to construct your tower.
2. Your tower must be transferred to the shelving for testing. Do not "mash" the clay onto this base to make it adhere. Your tower must be placed in the middle of the shelving, not at the ends.
3. Testing will be conducted as a group during the last half of the class. You will use a protractor to measure the angle of lean relative to the top of the shelving. Angles will increase in 10 °, beginning with 10°.

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Scoring Rubric

height,in meters	degree of tilt	performance points
h³1.5	20°	50 pts
h³1.5	10°	40 pts
h³1.5	0°	30 pts
1.0£h<1.5	30°	50 pts
1.0£h<1.5	20°	40 pts
1.0£h<1.5	10°	30 pts
1.0£h<1.5	0°	20 pts
0.5£h<1.0	40°	50 pts
0.5£h<1.0	30°	40 pts
0.5£h<1.0	20°	30 pts
0.5£h<1.0	10°	20 pts
0.5£h<1.0	0°	10 pts
h<0.5	50°	50 pts
h<0.5	40°	40 pts
h<0.5	30°	30 pts
h<0.5	20°	20 pts
h<0.5	10°	10 pts
h<0.5	0°	0 pts

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Data

Record the following data:

1. Number of straws used.
2. Average mass of one straw.
3. Mass of straws used.
4. Total mass of clay.
5. Mass of clay unused.
6. Mass of clay used.
7. Height of tower.
8. Degree of lean achieved.

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Questions

1. Calculate the total mass of your tower. Show all work.
2. Draw a diagram depicting your tower. Label all dimensions, including the base and its height.
3. Describe what you did to make your tower more stable. How did you arrange your straws? Why did you arrange them this way? Where did you place your clay? Why?
4. Use the concepts of torque and center of gravity to explain what made your tower fall.
5. What would you have done differently to produce a higher and more stable tower? Specifically describe what you would have done to the tower's center of gravity and how this would alleviate problems with torque.

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Project Evaluation

You will be awarded a maximum of 50 points for the performance of your tower.

You will record the required pieces of data for a maximum of 10 points.

You will answer the five questions for a maximum of 40 points.