Maximizing Pulley Performance: Uncovering the Truth with Capstan Equation Help"

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breid040
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Homework Statement
How does frictional force affect the tension on opposite sides of a pulley string?
Relevant Equations
Tload=Thold(e^uψ)
Hello,
I am doing a lab with 2 pulleys, layout shown below.
image

When I was analyzing the data, my actual values for displacement (d) consistently fell below my predicted values. I was wondering how the friction between the pulleys affected my displacement data. I did some research and came across the listed equation, the capstan equation. However, in order for friction to be the cause of this small error, the coefficient of friction would have to be 0.0024. Is that too small to be reasonable for a plastic pulley and a thread? Also, is using this equation applicable here? Thanks ahead.
 
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