Static Equilibrium - When will this guy bail off his ladder?

In summary, the conversation is about a window cleaner trying to determine the maximum length they can climb on a ladder before it slips. The ladder is placed against a frictionless wall at a 65 degree angle and rests on a wet floor with a coefficient of static friction of 0.40. Using equations and calculations, the answer was determined to be 9.41 meters, but there was some uncertainty about whether this was a reasonable answer due to the wet floor. Both parties ended up agreeing on the answer.
  • #1
wizzle
26
0

Homework Statement


A window cleaner of mass 95 kg places a 22kg ladder against a frictionless wall at a angle 65 degrees with the horizontal. The ladder is 10 m long and rests on a wet floor with a coefficient of static friction equal to .40. What is the max length that the window cleaner can climb before the ladder slips?


Homework Equations



sum F(x)=F(fr)-F(w)=0
sum F(y)=F(n)-mg=0
sum torque=F(w) * l (sin theta) - mg * 1/2 cos theta=0

(Using the point of the ladder on the ground as the pivot point)

The Attempt at a Solution




Using this equation: FW (10) sin(65) - 22 (9.8) (5) cos(65) - 95 (9.8)(x)cos(65) = 0

I then used Fr-Fw=0
Fn(Us) = FW
(1146.6*.40) = 458.64

I then input this into the equation

FW=22 [(9.8) (5) cos(65) - 95 (9.8)(x)cos(65)]/ (10) sin(65)

x = 9.41 m for the distance of the guy up the ladder. I've checked and re-checked and keep getting this answer, but intuitively it seems like that's too high since it's a wet floor that the ladder's on. Is the coefficient of static friction of 0.40 high enough to make this reasonable? Thanks for anyone who is willing to take a look!

-Lauren
 
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  • #2
Is the coefficient of static friction of 0.40 high enough to make this reasonable?
Not necessarily. It is the angle of ladder that prevents the slipping. Walking on the slippery floor we take smaller steps.
 
  • #3
Hmm..ok so being one who doesn't often hang out on ladders, I'm trying to figure out whether 65 degrees is enough to prevent slipping. Is it possible that 9.41 m would be a reasonable answer? I came out with the same answer after trying it multiple times, so I can't see where I could be going wrong. Thanks for anyone's opinion!
 
Last edited:
  • #4
What is the answer?
 
  • #5
Hi rl.bhat, the answer I came up with x=9.41 m on the 10 m ladder. What do you think?
Thanks!
-Lauren
 
  • #6
I too got the same answer. Is it wrong?
 
  • #7
yay! That's good news. I'm submitting it for an assignment so I'm glad to hear it!
I'll let you know whether it's right when I get it back :) Thanks for helping!
 

1. What is static equilibrium?

Static equilibrium is a state in which an object is at rest and not moving. This means that all forces acting on the object are balanced and the object will not accelerate or change its position.

2. How is static equilibrium related to the ladder example?

In the ladder example, the man is at rest on the ladder, indicating that the ladder is in a state of static equilibrium. This means that the forces acting on the ladder are balanced, with the downward force of gravity being counteracted by the upward force of the ladder against the wall and the man's weight on the ladder.

3. What factors can affect static equilibrium?

Static equilibrium can be affected by changes in the forces acting on an object, such as an increase or decrease in weight or a change in the direction or magnitude of a force. It can also be influenced by external factors, such as the presence of friction or air resistance.

4. How can we calculate when the man will bail off his ladder?

In order to calculate when the man will bail off his ladder, we would need to know the specific details of the ladder and the man's weight, as well as the forces acting on the ladder. Using Newton's laws of motion and the principles of static equilibrium, we could determine the point at which the forces are no longer balanced and the man would fall off the ladder.

5. What are some real-life examples of static equilibrium?

Static equilibrium can be observed in many everyday situations, such as a book resting on a table, a person standing still, or a bridge supporting the weight of cars and pedestrians. It is also important in engineering and construction, as structures must be designed to maintain static equilibrium in order to be stable and safe.

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