Towering Above

We hope the students will learn the basic concepts behind how forces are distributed in a tower.  Students will have a chance to use these principles to successfully design their own towers with a goal of making the tallest and strongest structure.

Materials:

• Skewers
• Gumdrops

Directions:

Design your own tower to hold the most weight and be the tallest.  A good start is to use the gum drops as “glue” to hold the skewers together.  Can your bridge sustain torsional forces?

# Questions Asked During the Experiment:

What makes the members capable of holding a lot of weight?

What are some good ways to connect the members so that the structure as a whole can hold a lot of weight?

How important is it to plan your structure before making it?

What kind of tests should you do to insure your design is sound?

Given more time how would you have improved your design?

# Explanations:

Center of Mass of 2D objects:

This is where we can think of all the mass being contained at. Easy examples: the center of a square, rectangle.  Basically, we should try to draw lines where the mass on each side of the line is the same (often symmetry lines in simple objects).  The center of mass is where these mass-balancing lines intersect.  More difficult examples: triangle, parallelogram.

Torque:

Torque is the product of the force and the moment arm (distance to the fixed part of the beam). Example: heavy and light person on seesaw. Light person (weight 50 lb) must sit twice as far as heavy person (weight 100 lb)

50lb * 2ft            =        100lb * 1ft

Similarly, beams within a tower experience torque from outside forces (such as weight pressing down, wind pushing from the side) We can see this when we bend a spaghetti or push a door open (this is why the handle is far away from the hinge! We need less force to get the same torque)

We can calculate the torque on both the tall and short beam:

Tall:    Torque = F * 2ft = 2F

Short  Torque = F * 1ft = 1F

So we get less torque for the short beam.  Beams often break at a certain value of torque that is characteristic of the material.  Therefore, to avoid breaking the beams, we should use shorter beams which can sustain larger forces!

Torque in 2D objects: which shapes are strongest?

What happens when we exert a sideways force on these two shapes?  The square will turn into a parallelogram and the triangle will retain its shape.  The triangle can do this because the diagonal beam pushes back against the force but the top horizontal beam in the square cannot.  We should use triangles whenever possible to increase the stability of our towers.