What is the minimum angle for a ladder to not slip against a frictionless wall?

[tigerwoods99]

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

 

[tiny-tim]

Hi tigerwoods99!

(have a theta: θ )

?? tan(theta) = .43?

The Attempt at a Solution

23.26

I don't think so.

What equations did you use?

 

[tigerwoods99]

Hi! I am really not sure its more or less a wild guess using trigonometric functions.

 

[tiny-tim]

(just got up :zzz: …)

Hi! I am really not sure its more or less a wild guess using trigonometric functions.

thought so!

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

how much is N? ​

 

[tigerwoods99]

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))

 

[tiny-tim]

τorque = 1/2mgx - FNx + Ffy

at max angle
μmgy = 1/2mgx

the maximum angle is θ = tan⁻¹(1/(2μ))

Yup!

Easy, isn't it? ​

 

[tigerwoods99]

haha yea i guess.. though i haven't learned this yet so i had to figure it out.