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

  • Thread starter tigerwoods99
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In summary, the problem involves a uniform ladder leaning against a frictionless wall at an angle θ and the goal is to find the minimum angle at which the ladder will not slip given a coefficient of static friction of 0.43. Using torque equations and trigonometric functions, the maximum angle can be calculated to be θ = tan−1(1/(2μ)).
  • #1
tigerwoods99
99
0

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
 
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  • #2
Hi tigerwoods99! :smile:

(have a theta: θ :wink:)
tigerwoods99 said:
?? 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
(just got up :zzz: …)
tigerwoods99 said:
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
tigerwoods99 said:
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.
 

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

What is an Equillibrium Ladder?

An Equillibrium Ladder is a scientific concept used to describe a system where opposing forces or factors are balanced, resulting in a state of stability.

How is an Equillibrium Ladder determined?

An Equillibrium Ladder is determined by calculating the forces or factors acting on a system and ensuring that they are equal and opposite, resulting in a net force of zero.

What are some examples of an Equillibrium Ladder?

Some examples of an Equillibrium Ladder include a seesaw, a balance scale, and a hanging mobile. In each of these examples, the forces acting on the system are balanced, resulting in a stable state.

Why is an Equillibrium Ladder important to understand in science?

Understanding the concept of an Equillibrium Ladder is important in science because it helps us understand the stability and balance of natural systems. It also allows us to predict how a system will behave when factors or forces are changed.

How is an Equillibrium Ladder related to other scientific principles?

An Equillibrium Ladder is closely related to the principles of Newton's laws of motion and the law of conservation of energy. It also plays a key role in fields such as mechanics, thermodynamics, and chemistry.

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