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Food for thought

## Problem

Please be aware that this resource is still in a somewhat draft form.

I slowly pull a weight along a (rough) table using a piece of string, moving my hand in a straight line.

This applet shows the situation in an ideal setting: the weight is at $P$, and the end of the string is at $A$. Move $A$ to see what happens. (Note that if you move $A$ backwards again in this applet, the weight simply retraces its path, which is not what would happen in reality.)

You can use the slider ($a$) to adjust the length of the string.

What is the shape of the path that the weight traverses?

If you would like some guidance, we offer two approaches to answering this question: Approach 1 and Approach 2.