### Introduction

When my physics students see these images, they cannot believe that they are actually looking at a REAL bridge. Most students (and the majority of people) think that structures are strong and built to last. Students don't realize that a structure must be designed to withstand different forces. Some forces are obvious and then some are not so obvious. Everybody knows that if you build a bridge and a truck drives across it, the bridge needs to hold the weight of the truck. How many students realize that the bridge is also supporting its own weight?!

Structures need to be designed to withstand other forces, too, besides just the weight of the objects that they hold. Engineers need to consider lots of forces and how they effect the structure that they are designing. They have to design bridges and buildings that can withstand forces due to wind, earthquakes, etc.

In this activity, students will design and build a support structure that will hold their Physics textbook. After this has been successfully accomplished, students enjoy holding a contest to determine whose structure can hold the greatest number of Physics books without collapsing. Winners can be determined two ways. Load the structures according to the directions. In the event of a tie, the winner is the lightest of the structures. For your more advanced students, the winner could be determined by using an "efficiency" calculation (mass held divided by mass of structure).

### Background

An object is in equilibrium when the net force acting on it is zero. Examine the forces acting. The weight of the object held is a force that acts downward. It is balanced by the normal force exerted on the object held by the structure. The normal force is a force that acts upward. As long as the weight (downward force) is balanced by the normal force (upward force), the net force acting on the object is zero and the object is in equilibrium. When an object is in equilibrium, there is no change in motion, so it is at rest (as in this case) or moves at constant velocity.

According to Newton's third law, the normal force exerted by the structure on the object is equal in magnitude, but opposite in direction, to the weight of the object. In other words, the normal force that the structure exerts on the object is equal to the weight of the object until the structure fails.

According to Newton's second law, a net force causes an object to accelerate. In this case, the sum of the normal force and the weight is zero represents the net force acting on the object. There is no acceleration and the object remains in equilibrium.

When the object falls, breaking the structure, the normal force exerted by the structure was insufficient to offset the weight of the object. The net force is no longer zero. The weight of the object is greater than the normal force. Now, the object accelerates downward (in the direction of the greater weight) until it strikes a surface whose normal force will balance the object's weight.

### Prerequisites

Students must be familiar with terms such as force, normal force, and weight. Students must be familiar with Newton's three laws of motion.

### Objectives

• To design a structure capable of holding a textbook using the materials supplied.
• To demonstrate that the weight of a textbook is offset by the normal force exerted on the book by the structure.
• To estimate the normal force exerted by the structure on the textbook the instant before structural failure.
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### Materials

• 20 pieces of dry fettucini
• one meter of masking tape
• meter stick
• piece of paper
• lightweight book
• medium weight book
• Physics textbooks

### Design Requirements

1. The height of the structure shall be at least 5 cm, supporting the book 5 cm above the table. All parts of the book should be supported at least 5 cm above the table.
2. The structure shall use all or part of the 20 pieces of fettucini and all or part of the 1 m of masking tape. No additional tape or pasta may be used.
3. Tape must be used to secure the support structure. The structure must be one unit that can be picked up and placed on the testing area. Overlapping, non-taped pieces of fettucini are not allowed. Any or all versions of a "column" of fettucini pieces circled by tape are not allowed. A "log cabin" type structure consisting of overlapping, taped pieces of fettucini is not allowed.
4. The structure must have a minimum of three points of support.

### Procedure

1. Design and build a support structure according to the design requirements
2. Measure and record the mass of the structure. Measure and record the masses of the paper, the lightweight book, the medium weight book, and one Physics textbook.
3. Measure and record the dimensions of the structure. Note minimum height.
4. The students will test the integrity of the pasta structure by placing the piece of paper on the structure first. The paper is removed, and the lightweight book is placed on the structure. The lightweight book is removed, and the medium weight book is placed on the structure. Last, the medium weight book is removed and the Physics book is placed on the structure. To be successfull, the structure must hold the item for ten seconds.
5. Students who successfully hold the Physics book for the required amount of time will be allowed to compete in the contest.
6. Continue loading the structure with Physics books until structural failure occurs.

### Questions

1. Calculate the weight of the object(or objects) held just prior to structural failure. Calculate the normal force exerted by the structure just prior to ` structural failure.
2. Calculate the efficiency of your structure by comparing the maximum mass held by the structure to the structure's mass.
3. What happens to the structure when the normal force is less than the object's weight?
4. Which part of your structure broke or collapsed first? Why do you feel the structure broke or collapsed at this point? What would you do to make your structure stronger at this point?
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## Item Held

Piece of Paper
10 points
Lightweight Book
20 points
Medium Weight Book
30 points
Physics Book
40 points

### Project Extension

You don't associate a bridge with a dinosaur, but using physics to compare their structures explains much of the dinosaur's morphology.

In this part of the project, students will acquire information from Internet sources, enabling them to compare and contrast the structure of a bridge and that of a dinosaur.

### Project Evaluation

"Bridge"
40 points maximum
Questions
20 pts maximum
Extension
40 pts maximum

### Tutorial

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Here are some practice problems dealing with weight, mass, and Newton's second law (permission granted for inclusion of these problems by S. Sanders).

### Bridge-Building Tutorial

Permission granted for its inclusion by NOVA.