So I've been trying to secure a large box to the ceiling of my garage. I currently have the rope passing directly over a pole attached to the ceiling. This takes a LOT of effort to pull the weight up, so I'm going to invest in a pulley. Whilst a single pulley won't hold any mechanical advantage, it will negate the strong forces of friction in play. I estimate the coefficient of friction to be about 0.8 between the rope and the pole (nylon on rubber).

I was curious how much extra force I was having to apply, so I started playing around with the capstan equation. If I've done my maths correctly, I've calculated that the force required to hold the box up is about a 10th of the weight of the box. This feels about right.

However, my question is, how much force do I need to apply on the T(hold) end, in order to induce slip? I.e. How much more force than 199N will I need to apply to lift the box?