# Maximizing Ladder Stability: Understanding the Principle of Moments

• TheRealSJ
In summary, the student is not sure how to approach the problem and is struggling to understand the instructions.
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 said:
In order to receive help, you must show some effort. "I have no clue" is no effort.
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?

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

hutchphd and TheRealSJ
berkeman said:
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.

berkeman
kuruman said:
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

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

TheRealSJ
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.

TheRealSJ
TheRealSJ said:
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.

Last edited:
TheRealSJ, Lnewqban and ChiralSuperfields
haruspex said:
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.

ChiralSuperfields

## 1. What is the principle of moment?

The principle of moment, also known as the law of moments, is a fundamental concept in physics and engineering that states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.

## 2. How is the principle of moment used in real-life situations?

The principle of moment is used in various real-life situations, such as designing structures like bridges and buildings, calculating the weight distribution of objects on a seesaw, and determining the torque needed to loosen a bolt.

## 3. Can you explain the mathematical equation for the principle of moment?

The mathematical equation for the principle of moment is M = F x d, where M is the moment, F is the force applied, and d is the distance from the pivot point to the line of action of the force. This equation shows that the moment is directly proportional to the force and the distance from the pivot point.

## 4. What is the difference between the principle of moment and the principle of torque?

The principle of moment and the principle of torque are essentially the same concept, with the only difference being the units used. The principle of moment is typically used in statics and engineering, while the principle of torque is used in dynamics and rotational motion.

## 5. How does the principle of moment relate to Newton's laws of motion?

The principle of moment is a direct result of Newton's first law of motion, also known as the law of inertia. This law states that an object at rest will remain at rest unless acted upon by an external force. The principle of moment ensures that an object in rotational equilibrium will remain in that state unless acted upon by an external torque.

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