Falling Beads

Suppose that you have a large number of knitting needles and thousands of beads which can slide along needles without friction. All beads are released from rest at the same time from a point A to slide down the needles.

• Find a shape which is formed by the beads after time $t$.
• Describe how this shape is changing with respect to time.

Extension: In a real situation there will a friction force. The coefficient of friction is $\mu$. Suppose it is not dependent on the speed of a bead. Find the shape of beads after time $t$ and describe how it is changing.