Solve Ladder Problem: 4 Equations, 5 Unknowns

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Homework Help Overview

The problem involves a uniform ladder leaning against a smooth wall, with various forces acting on it. The original poster seeks to determine the vertical thrust by the ground, the horizontal push by the wall, and the coefficient of friction between the ladder and the ground, while noting that they have four equations and five unknowns.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the vertical force (V) and the normal force (N), questioning whether they represent the same force. There is also a consideration of the implications of the wall being smooth on the forces involved.

Discussion Status

Participants are actively engaging with the original poster's equations and assumptions. Some have provided clarifications regarding the forces acting on the ladder, suggesting that the vertical force may be zero due to the wall's smoothness, which reduces the number of unknowns to three.

Contextual Notes

The original poster mentions having four equations and five unknowns, indicating a potential gap in the information needed to solve the problem. The discussion also highlights the importance of careful reading of the problem statement and the definitions of the forces involved.

Michael94
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Homework Statement


Uniform ladder leaning 60 degrees from the ground against smooth wall (ladder: length 10' weight 60#). Vertical thrust by ground ? Horizontal Push by wall ? Coeff. of friction between ladder and ground ?


Homework Equations


Fx = 0 = F + H = 0
Fy = 0 = V + N - 60# = 0
L about ladder center of gravity = 0 = V*sin60*5' + H*cos60*5' - N*sin60*5 + F*cos60*5' = 0
Friction Coefficient = F/N
I have 4 equations and 5 unknowns. What am I missing in order to find the results ?


The Attempt at a Solution

 
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Welcome to PF!

Hi Michael! Welcome to PF! :smile:
Michael94 said:
I have 4 equations and 5 unknowns.

ah, but your V and your N are the same :wink:
 
I don't understand why V = N. Sum of the forces in the vertical direction w/ origin @ ladder center of gravity V + N = 60#, right ?
 
Michael94 said:
I don't understand why V = N.

V and N are your names …

what are they supposed to be?

If V is the vertical force on the ladder from the ground, and if N is the normal force, they're just different names for the same thing, aren't they? :confused:
 
I attached the ladder illustration here, maybe you are able to make better sense of the problem.
 

Attachments

  • LadderLoad.jpg
    LadderLoad.jpg
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It is a smooth wall, so V = 0. So you only have 3 unknowns (F, N, H) and 3 equations

If wall is not smooth then you need another equation that involves the elastical behavior of the ladder.
 
Hi Michael! :smile:

Yes, venkatg :smile: is right … your V = 0.

(which is why it never occurred to me that your V was at the top of the ladder :wink:)

Moral: read every word of the given question carefully (and write your own question carefully!)
 

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