# Do you have an idea for two easy experiments to measure the coefficients of static and sliding friction of a rope wrapped around a steel rod?

I'm researching a phenomenon dependent on the Capstan/Euler-Eytelwein-Equation. To model a simulation, I need the friction coefficients. I came up with the idea of hanging one mass $$m_1$$ on one side of the rope, and another mass $$m_2=4m_1$$ on the other one, then wrapping the rope around the rod (with an angle of $$\frac {\pi}{2}$$ and letting the system slide down. By measuring the time it took $$m_2$$ to traverse a certain distance I can compute the acceleration acting on the system. By comparing it to the frictionless case I get the force of friction. Does this sound sensible? But what could I do for static friction?

• Why $m_2=4m_1$? Is there something special about 4? then wrapping the rope around the rod (with an angle of $\pi/2$) Why $\pi/2$? That's 90 degrees. Do you really mean $\pi$, which is 180 degrees? Could you give us a link or a reference for the Capstan/Euler-Eytelwein equation, or state what the equation is? Are you referring to the fact that tension varies as $e^{\mu\theta}$?
– user4552
Mar 6, 2019 at 6:57
• Yes I am referring to this exponential behaviour. I choose the ratio of ~1:4 because then the process takes long enough to be measured quite accurately. Mar 6, 2019 at 7:25

I did experiments using 6 mm nylon cord with a kernmantle construction, running over cylindrical metal rods with a diameter of roughly 5-10 mm (similar to some materials used in rock climbing). With these materials, I did not get good quantitative agreement with the rule that tension varies as $$e^{\mu\theta}$$.