Uniformly Unstable

Stage: 5 Challenge Level: Challenge Level:1

Why do this problem?

This problem is great for stimulating discussion at the start of a mechanics course.

 

Possible approach

This problem is easy to introduce to a class according to the order suggested in the problem, but you might like to keep the existence of the Gombocs as a surprise. As you lead the exploration, be on the lookout for opportunities to introduce and reinforce key concepts and vocabulary as students strive to articulate their thoughts. Examples might include: uniform density; equilibrium; perturbation; stability; symmetry; mathematical model; configuration; static; centre of mass; magnitude; vectors and forces. Preparing the ground in this way before rushing into content is time well spent!

Throughout, demand clarity of thought and speech.

 

Key questions

Tell me what you are thinking!
Can you draw a clear diagram?
 

Possible extension

 
Sufficient extension is built into this task!
 

Possible support

 
Restrict attention to cuboids, paying attention to 'long and thin' and 'nearly cubic' solids.