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Dear all,

Happy New Year!

2006 brings the mathematical theme of Mechanics to the NRICH website 
(http://nrich.maths.org).  Our balance environment provides you with a rich 
resource in which to explore this topic and many of the problems make use 
of it.

We might associate mechanics with mathematics at a high level but there is 
plenty of scope for tackling some aspects if you're at primary school and 
there's a great opportunity to overlap with science.  Explore the cogs 
interactivity in Turning Cogs 
(<http://nrich.maths.org/public/viewer.php?obj_id=4771>) and see if they 
can deduce how they interlock.  Why not try Weighted Numbers 
(<http://nrich.maths.org/public/viewer.php?obj_id=4726>) - can you work out 
where to hang the numbered weights so that it balances?

For more of a challenge, Balance 1 
(<http://nrich.maths.org/public/viewer.php?obj_id=4342>), Balance 2 
(<http://nrich.maths.org/public/viewer.php?obj_id=4343>) and Balance 3 
(<http://nrich.maths.org/public/viewer.php?obj_id=4344>) will be worth a 
look.  You can use the environment to find out where Meg should place her 
pouch of marbles so that it balances with Mo's.  Can you predict how many 
marbles Mo would need if Meg's pouch were 75cm from the centre?

Inside Outside (<http://nrich.maths.org/public/viewer.php?obj_id=4767>) 
takes these ideas a bit further and requires the use of algebra to find 
arrangements of weights that balance.  Whoosh 
(<http://nrich.maths.org/public/viewer.php?obj_id=4755>) describes two 
balls in a frictionless shute.  How far does a ball at the bottom of the 
shute travel horizontally before it hits the ground once a second ball at 
the top of the shute collides with it?

We hope you find motivating and challenging problems to keep you busy and 
look forward to receiving your solutions.

With best wishes from the NRICH Team.

Liz Pumfrey
NRICH Primary Teacher Research Associate
University of Cambridge Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WA
01223 764246
www.nrich.maths.org

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