While looking for interesting problems, I was led to a problem involving infinite pulleys.(adsbygoogle = window.adsbygoogle || []).push({});

The problem and solution can be found http://www.feynmanlectures.info/solutions/infinite_pulleys_sol_1.pdf" [Broken]. Now I follow the solution up to the part where he claims [itex]\frac{1}{4^{i}M_i}[/itex] is always vanishing (tends to 0) as i approaches infinity. This does not seem valid.

From [tex]M_{i-1} = \frac{4M_{i}t^{i-1}}{M_i + t^{i-1}}[/tex] we have

[tex]M_{i-1}=\frac{4t^{i-1}}{1 + \frac{t^{i-1}}{M_i}}[/tex]

Since we know [tex]\frac{t^{i-1}}{M_i} \ge 0[/tex] we then have

[tex]M_{i-1} \le 4t^{i-1}[/tex] or equivalently

[tex]M_i \le 4t^i[/tex]

from this we can get

[tex]\frac{1}{4^{i}M_i}\ge \frac{1}{4}\cdot\frac{1}{4^{i}t^{i}}[/tex]

so that [itex]\frac{1}{4^{i}M_i}[/itex] is vanishing only if [itex]\frac{1}{4^{i}t^{i}}[/itex] is. I'm not sure how to determine the actual convergence of the M_{i}s and I might be missing something but this solution does not seem to be valid because of the above point. Does anyone know of a way to perhaps salvage this solution?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Feynman's Infinite Pulley Problem

**Physics Forums | Science Articles, Homework Help, Discussion**