# Spyrals!

A hose of mass $$M$$ and length $$L$$ is made into a coiled roll of radius $$R$$. The hose is then unrolled across a level ground with initial speed $$v_0$$, while the free end is held at a fixed point on the ground. The hose unrolls and becomes straight.

Determine the time taken by the hose to completely unroll.

Details and Assumptions

• $$R\ll L$$.

• At all instant, the hose is performing pure rolling.

• The hose is arbitrarily flexible.

• The work necessary for its deformation, air resistance and rolling resistance can be neglected.

• $$L = 100 \text{ m}, \ v_0 = 7\text{ ms}^{-1}$$.

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