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sncobra
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Homework Statement
[/B]
A 3.0-m-long ladder, as shown in the following figure, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.32.
What is the minimum angle the ladder can make with the floor without slipping?
Homework Equations
With the axis of rotation at the bottom of the ladder:
ΣT = 0 <- torque
ΣF = 0
T = LF
T = LFsinφ
ƒ = μN
The Attempt at a Solution
X to the right is positive, Y up is positive
Nw = Normal of wall
Nf = normal of floor
fs = static friction force
Fg = gravity
ΣFx = 0
Nw - fs=0
Nw = μNf
ΣFy = 0
Nf-Fg = 0
Nf = mg
So,
Nw=μmg
Now I'm still having trouble with torques so bear with me. Since these two forces go through the axis then they produce no torque correct?
TNf = 0
Tfs = 0
and
TFg = (Fg)(L/2) = mg(L/2)
TNw = (Nw)(L)
Am I on the right path? I think you sum the two torques but I don't have the mass so that wouldn't work.
Also, how do I know if the torque is negative or positive? and which way do I make torque positive? CW or CCW?
Appreciate any and all advice :)
link to the picture: http://session.masteringphysics.com/problemAsset/1385677/5/K-P12.60.jpg