Maximizing Ladder Stability: Understanding the Principle of Moments

[TheRealSJ]

Homework Statement

A 100N uniform ladder of length 8m rests against a smooth vertical wall. If the force of friction between the ladder and wall is 40N, what is the maximum angle the ladder can make with the floor before it slips?

Relevant Equations

Sum of moments clockwise = Sum of moments counterclockwise

Just started this topic in my advanced physics class and to be honest i have no clue how to really approach this question

 

[kuruman]

In order to receive help, you must show some effort. "I have no clue" is no effort.
Please read, understand and follow our homework guidelines here
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[TheRealSJ]

In order to receive help, you must show some effort. "I have no clue" is no effort.
Please read, understand and follow our homework guidelines here
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Ok well "I have no clue" may have been a slight exaggeration but I'm not sure if my initial steps were in the right direction. What I did was:
M40 (M=moment) + Rw (reaction force of wall) = M100, as counter clockwise sum of moments = clockwise sum of moments but then I have no known angle to find the perpendicular distance from the pivot (which in this scenario I made the corner of the floor and wall) , apart from the axiomatic 90 degree formed with wall and floor, so I don't know what to do next?

 

[berkeman]

They only give you the friction with the wall and not the floor? Weird...

 

[kuruman]

They only give you the friction with the wall and not the floor? Weird...

Yes, that is problematic because the vertical wall is said to be "smooth" which means no friction. Yet the statement says that there is 40 N worth of friction between the ladder and the wall. Maybe it's a typo and the friction is between the ladder and the floor. @TheRealSJ please check the statement of the problem as was given to you.

 

[TheRealSJ]

Yes, that is problematic because the vertical wall is said to be "smooth" which means no friction. Yet the statement says that there is 40 N worth of friction between the ladder and the wall. Maybe it's a typo and the friction is between the ladder and the floor. @TheRealSJ please check the statement of the problem as was given to you.

Hmm I have checked the question again and it matches up with what I typed up here. Maybe my prof did a typo, I'll email him about it thanks

 

[berkeman]

You'll get extra credit for being the first student to notice the typo...

 

[kuruman]

And while you're asking, also ask whether the 40 N is the force of friction at the moment the ladder is just on the verge of slipping. The statement of the problem is not clear on that point.

 

[haruspex]

Hmm I have checked the question again and it matches up with what I typed up here. Maybe my prof did a typo, I'll email him about it thanks

If you lean a ladder against a wall and the floor is perfectly smooth it will always slip, so the friction must be from the floor.

Even then the question is a little odd. Since you are given the magnitude of the frictional force you can deduce the angle regardless of whether it is on the point of slipping. Presumably it intends that 40N is the maximum frictional force. Yet even that is weird, implying it does not depend on the normal force.

You might also point out that it asks "what is the maximum angle the ladder can make with the floor before it slips?" Can it slip from being too upright?

Prof had a late night, perhaps.

 

[kuruman]

You might also point out that it asks "what is the maximum angle the ladder can make with the floor before it slips?" Can it slip from being too upright?

Good point. I missed that.