Equillibrium Ladder

  • #1

Homework Statement


A uniform ladder of mass m and length L leans at an angle θ against a frictionless wall, Fig. 9-61. If the coefficient of static friction between the ladder and the ground is 0.43, what is the minimum angle at which the ladder will not slip?

Pic:
http://www.webassign.net/giancoli5/9_61.gif


Homework Equations



?? tan(theta) = .43?

The Attempt at a Solution



23.26
 

Answers and Replies

  • #2
tiny-tim
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Hi tigerwoods99! :smile:

(have a theta: θ :wink:)
?? tan(theta) = .43?

The Attempt at a Solution



23.26
I don't think so.

What equations did you use?
 
  • #3
Hi! I am really not sure its more or less a wild guess using trigonometric functions.
 
  • #4
tiny-tim
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(just got up :zzz: …)
Hi! I am really not sure its more or less a wild guess using trigonometric functions.
thought so! :rolleyes:

ok … call the normal reaction force (from the ground) N, and the horizontal reaction force H …

how much is N? :smile:
 
  • #5
I think this is right.


τorque = 1/2mgx - FNx + Ffy

at max angle
μmgy = 1/2mgx

the maximum angle is θ = tan−1(1/(2μ))
 
  • #6
tiny-tim
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τorque = 1/2mgx - FNx + Ffy

at max angle
μmgy = 1/2mgx

the maximum angle is θ = tan−1(1/(2μ))
Yup! :biggrin:

Easy, isn't it? :wink:
 
  • #7
haha yea i guess.. though i haven't learned this yet so i had to figure it out.
 

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