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# Crushing & Toppling Towers

A simple practical exercise to perform at home in your kitchen on the loads required to cruch and topple towers of cheese.

## Introduction

You should be able to perform this exercise in your kitchen using the equipment usually found there plus a block of processed cheese.

## Objective

To estimate the critical height of a tower at which its collapse behaviour changes mode.

## Apparatus

You will need a sturdy table or bench. A handy-sized spatula with a smooth, flat, rigid surface1. A set of kitchen scales with a flat horizontal surface2. A block of hard, processed cheese cut into about a dozen 1cm3 cubes – use the cheapest, most processed cheese available3.

## Procedure

1. Place a single cube on the scales and note the reading on the scales. Slowly compress the cube with the spatula. Observe how the cube deforms and eventually fails by crushing. Note the reading on the scales when it starts to fail, , i.e. when it begins to undergo large-scale yielding and deformation.
2. Repeat the process described in paragraph 1 but for two fresh cubes stacked on top of one another. Subsequently, repeat the process for progressively more fresh cubes stacked in a tower until the tower fails by a cube sliding sideways. Note the critical number of cubes at which the failure mode of the tower changes from crushing of a cube to buckling of the tower.
3. Build a new tower with as many cubes as possible before the tower topples over of its own accord. Note the critical number of cubes at which the tower topples over spontaneously.
4. On a bar chart, plot your failure loads [readings from the scales] as a function of tower height [number of cubes].

## Discussion/Analysis

In an ideal world, your tower should be in static equilibrium so that it will not topple over and it would always fail by a cube being crushed. However, we do not live in an ideal world and either your tower will not be perfectly vertical (especially if you did not cut your cubes carefully) or the applied load will not be exactly vertical and at the centre of the tower, or both. Consequently, there is always some magnitude of force causing a moment and a rotational deformation on the tower. The sensitivity to toppling increases as more cubes are added to the tower until eventually the external force required is zero and the gravitational force on the cubes is sufficient to cause collapse of tower, as it seeks to minimise its potential energy.

## Conclusions

What were the critical heights of the tower at which its failure mode changed? How did the failure load change as the tower became taller? How accurate was your experiment? You could repeat each step six times (using fresh cubes) to obtain six values for each parameter and then plot the mean value, in which case the standard deviation on this mean will be an indication the error in the experiment.

## How did you do?

We would love to know your results, you can post them in the comments section below.

Why not take photos of you carrying out your experiment and then post them to our media wall? You can also add a video to the media wall by uploading it to YouTube (or another social media site) and then cutting and pasting the embed code.

2 I used a flat digital scale similar to this one: http://www.amazon.co.uk/Salter-1036-Electronic-Kitchen-Silver/dp/B001MF3C4S

3 I used a block of processed cheddar cheese [about 250g] and a large sharp knife to cut it into cubes. It took several attempts to achieve regular well-formed cubes.