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# More Bridge Building

Although this problem is quite open ended, the key objective is for students to engage with the distribution of tensions and compressions in a structure as a geometric whole, rather than focussing on the algebra of a typical calculation. Students should learn the power of vector methods to understand the mathematical structure of a problem. Once they develop a feel for the ideas they should be able to create general statements about structures without the need for calculation from the onset. This interplay between geometrical and algebraic arguments is a very important skill for students to begin to develop.

The ideas covered in this problem extend to more challenging investigations of real world structures. Great examples are Forth Bridge in Scotland, the Eiffel Tower and geodesic domes. These can be used to stimulate discussion about the forces in real bridges and structures.

Questions that you may like to pose are: What structural similarities do real world structures have? Why do you think that they share these similarities? Why do you think that the designers chose these structures? How does changing the structure change the location of the greatest tensions and compressions? How do you think the forces are distributed amongst all of these objects? Will there be any net forces at the joints?

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Age 16 to 18

Challenge Level

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Although this problem is quite open ended, the key objective is for students to engage with the distribution of tensions and compressions in a structure as a geometric whole, rather than focussing on the algebra of a typical calculation. Students should learn the power of vector methods to understand the mathematical structure of a problem. Once they develop a feel for the ideas they should be able to create general statements about structures without the need for calculation from the onset. This interplay between geometrical and algebraic arguments is a very important skill for students to begin to develop.

The ideas covered in this problem extend to more challenging investigations of real world structures. Great examples are Forth Bridge in Scotland, the Eiffel Tower and geodesic domes. These can be used to stimulate discussion about the forces in real bridges and structures.

Questions that you may like to pose are: What structural similarities do real world structures have? Why do you think that they share these similarities? Why do you think that the designers chose these structures? How does changing the structure change the location of the greatest tensions and compressions? How do you think the forces are distributed amongst all of these objects? Will there be any net forces at the joints?

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

A cone is glued to a hemisphere. When you place it on a table in what position does it come to rest?

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.