Find Coefficient of Friction for Firefighter on Ladder

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Homework Help Overview

The problem involves a uniform ladder leaning against a frictionless wall, with a firefighter standing on it. The objective is to determine the coefficient of friction between the ladder and the floor, given specific weights and distances.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss drawing free-body diagrams and applying Newton's laws in both horizontal and vertical directions. Some express difficulty in managing the complexity of the problem due to multiple unknowns. Others attempt to derive the coefficient of friction using trigonometric relationships based on the ladder's angle.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have provided guidance on setting up the problem, while others are grappling with the complexity of the calculations. There is no explicit consensus on the method or solution yet.

Contextual Notes

One participant notes that this problem was encountered on a test, indicating a potential pressure to understand the material. The setup includes specific measurements and conditions that may influence the calculations.

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Homework Statement


(8 marks)
A uniform ladder (m = 35kg) leans against a smooth frictionless wall. The foot of the ladder is 3 m from the wall and an 85kg firefighter stands 3m up the ladder as shown. Find the coefficient of friction of the floor.
http://i49.tinypic.com/ftdo9g.jpg

Homework Equations


(Angular Newton's Second Law and Linear Newton's First Law)
Στ=0 and ΣFx=ΣFy=0
τ = F⊥r

The Attempt at a Solution


 
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Draw a free-body diagram of the ladder, being sure to include all forces. Then write out Newton's second law for both the horizontal and the vertical directions. For torque, choose a point and write out the rotational analogue of Newton's second law about that point.
 
i've tried that, and it gets so complicated and there are so many unknown variables that I get lost every single time. this was actually on my test and i got 0.
 
ladder is 3m from wall...it connects with the wall 4m high...so get the angle which is tan^-1 of 4/3...which is 53.1

then tan53.1=2umg/mg...which is equal to 2u..
tan53.1/2=coefficient friction=.67

i think that's how you do it
 

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