# Slippery Pulley!

**Classical Mechanics**Level 5

A heavy, long, inelastic chain of length \(L\) is placed almost symmetrically onto a light pulley which can rotate about a fixed axle, as shown in the figure. If :

**I**) It's velocity when it leaves the pulley can be represented by \(v_{break} = \dfrac{L^wg^x}{y}\)

**II**) And height \(h\) climbed by the end which is going up before losing contact of the pulley can be represented as \(h_{break} = \dfrac{L}{z}\)

Evaluate \(\large \dfrac{w+x}{2} + y + z +1\)

**Assumumptions**

- Take the pulley to be massless and thus performing pure rolling.
- The chain goes up due to slight asymmetry.
- \(w,~x,~y\) and \(z\) are numerical constants \(\in \mathbb{N}\) and
**can**have any value! - Take radius \(R\) of the pulley to be very small, i.e. \(R\ll L\)