# How Do Friction Forces Act on a Ladder Leaning Against a Wall?

• minimario
In summary: Context is everything.In summary, when a ladder is leaning against a wall with friction both on the wall and against the ground, the direction of the friction forces can be determined by analyzing the various factors such as the weight of the ladder, the coefficient of static and dynamic friction, and the presence of any additional loads or external forces. Context is important in solving such problems, and making assumptions is necessary to simplify the problem and determine the direction of the forces accurately.
minimario

## Homework Statement

When a ladder is learning against a wall with friction both on the wall and against the ground, how do you determine the direction of the 2 friction forces?

## The Attempt at a Solution

[/B]
I found a pic online, why is this true?

Look at the diagram - which way is the ladder going to slide?
What does the friction do to the rate the ladder slides?
Which direction does the friction have to point to do that?

This is actually a harder question than it might appear. The problem is, you have to make assumptions about the nature of the way the ladder is placed on the wall.

Suppose you start the ladder close to vertical and resting on the ground. Then you ever so gently and slowly lean it over until it touches the wall. At this point, there will be very little vertical force at the contact point with the wall. The contact point with the ground has to provide all the friction required to prevent sliding.

Now, let a painter climb up the ladder. He will bend the ladder slightly so the upper end moves down the wall slightly. So there will be frictional force involved, and it will of course point in the direction opposite to the motion. But as to how big this force is, it depends on how big the guy is and how springy the ladder is. And the coefficient of static and dynamic friction of the wall and the ladder. And probably a couple other things I'm not thinking of just now. But it will resist the bowing of the ladder to some degree.

Now let the guy get off the ladder again. The bowing will spring back. And the upper end of the ladder will move up the wall. And there will be friction force in the other direction. This friction will resist the "springing back" of the ladder to some degree.

It's an interesting question to think about. How much "bow" can the friction with the wall sustain? Some interesting geometry in there to resolve the forces.

haruspex
DEvens said:
This is actually a harder question than it might appear. The problem is, you have to make assumptions about the nature of the way the ladder is placed on the wall.

Suppose you start the ladder close to vertical and resting on the ground. Then you ever so gently and slowly lean it over until it touches the wall. At this point, there will be very little vertical force at the contact point with the wall. The contact point with the ground has to provide all the friction required to prevent sliding.

Now, let a painter climb up the ladder. He will bend the ladder slightly so the upper end moves down the wall slightly. So there will be frictional force involved, and it will of course point in the direction opposite to the motion. But as to how big this force is, it depends on how big the guy is and how springy the ladder is. And the coefficient of static and dynamic friction of the wall and the ladder. And probably a couple other things I'm not thinking of just now. But it will resist the bowing of the ladder to some degree.

Now let the guy get off the ladder again. The bowing will spring back. And the upper end of the ladder will move up the wall. And there will be friction force in the other direction. This friction will resist the "springing back" of the ladder to some degree.

It's an interesting question to think about. How much "bow" can the friction with the wall sustain? Some interesting geometry in there to resolve the forces.
I agree with all that, but I'd like to go into a couple of details.
As the painter starts to climb the ladder, static friction will initially stop the top end sliding. Assuming it does eventually slide, it will only slide to the point where kinetic friction is sufficient to maintain balance (I'm ignoring momentum). Similarly on the descent, so it is highly likely that after the painter has stepped off the ladder the friction from the wall acts downwards. It will be static friction, but the force's magnitude will correspond to the kinetic coefficient.

This is why the context is important.
There are no physics problems where you do not need to , make some assumptions.

In the above, there is no mention of additional loads on the ladder, so assuming no painter is reasonable. None of the other points make any difference to the question actually stated... re: direction of the friction force. This one only makes a momentary difference... these problems usually concern either a static equilibrium or the ladder is sliding.

All that has been demonstrated is that it is possible to complcate the problem by adding extraneous influences. This is always possible. But if it is not in the problem statement, you need a reason to include it.

It does not matter how little friction is present at the contact points... the context is for working it out: which way you draw the arrows? It may well be that a valid approximation can be made taking one friction force to be zero... however, the supplied diagram does not support this.

... and so on.
Context is everything.

Simon Bridge said:
This is why the context is important.
There are no physics problems where you do not need to make some assumptions.

In the above, there is no mention of additional loads on the ladder, so assuming no painter is reasonable. None of the other points make any difference to the question actually stated... re: direction of the friction force. This one only makes a momentary difference... these problems usually concern either a static equilibrium or the ladder is sliding. There are many ways to bring extraneous influences into complicate the problem... but these are not in the problem statement.

It does not matter how little friction is present at the contact points... the context is for working it out: which way you draw the arrows? It may well be that a valid approximation can be made taking one friction force to be zero... however, the supplied diagram does not support this.

... and so on.
Context is everything.
I think you are missing the point of the imaginary painter argument. It demonstrates that there is insufficient information to determine which way the frictional force from the wall points. There is a continuum of possibilities consistent with the statics equations.

haruspex said:
There is a continuum of possibilities consistent with the statics equations.
If you treat the ladder as rigid, then would it be impossible for the frictional forces to point the other way?

Nathanael said:
If you treat the ladder as rigid, then would it be impossible for the frictional forces to point the other way?
It doesn't solve the problem that there is a range of solutions to the equations. If there is sufficient coefficient of static friction from the ground, that range will include a downwards frictional force from the wall. In the real world (where nothing is completely rigid), this is resolved by the history (Simon's 'context').

The centre of mass of the adder is falling so the top of the ladder must also be moving down and the bottom of the ladder must be moving to the right. The frictional forces must try and oppose this motion and so must be acting upwards at the top of the ladder and to the left at the bottom of the ladder.

Farcher said:
The centre of mass of the adder is falling
No, the question as stated is about static friction, so nothing is falling. If it were kinetic friction then all the complications discussed above would go away and your analysis would be correct.

minimario said:

## Homework Statement

When a ladder is learning against a wall with friction both on the wall and against the ground, how do you determine the direction of the 2 friction forces?

The dirction of the friction force at the ground is easy...

The ladder isn't accelerating horizontally so the horizontal components of all forces on the ladder must sum to zero. At the top of the ladder there is a component force to the right (R_2) so the friction force with the ground (F_1) must be equal but to the left.

Others have explained that the direction of friction with the wall is hard or impossible to determine but typically real ladders bend as you climb up and sometimes the foot sinks into soft ground a bit. So the top of the ladder tends to be dragged down the wall a bit. Thus it's reasonable to assume friction there acts upwards.

Typically problems will ask how far up a wall can you climb before the ladder slip down so the above is a reasonable assumpion. However it would be different if they asked you for the force required to push a ladder up a wall or something like that. Read the question carefully.

CWatters said:
The dirction of the friction force at the ground is easy...
The thread is over three years old. It was resurrected in post #9 with a claim that the friction at the top must be acting up, which is not necessarily true.

haruspex said:
The thread is over three years old

Missed that.

## 1. What is a ladder against a wall?

A ladder against a wall is a common tool used for climbing or reaching higher places. It consists of two parallel side pieces connected by rungs or steps, with one end placed against a wall for support.

## 2. How do you safely use a ladder against a wall?

To safely use a ladder against a wall, make sure it is placed on a stable and level surface. The base of the ladder should be one quarter of the working length away from the wall. Always face the ladder while climbing and maintain three points of contact at all times. Do not overreach and make sure the ladder is securely fastened at the top.

## 3. What are the different types of ladders against a wall?

There are several types of ladders against a wall, including step ladders, extension ladders, and multi-purpose ladders. Step ladders are self-supporting, while extension ladders lean against a wall and can be adjusted to different heights. Multi-purpose ladders can be used in various configurations, including against a wall.

## 4. How do you choose the right ladder against a wall for a specific task?

The right ladder against a wall for a specific task depends on the height you need to reach and the type of work you will be doing. Step ladders are best for tasks at lower heights, while extension ladders are suitable for higher tasks. Multi-purpose ladders are versatile and can be used for a range of tasks.

## 5. What are some safety precautions to take when using a ladder against a wall?

When using a ladder against a wall, always inspect it for any damage or defects. Make sure the ladder is the correct height for the task and that it is properly secured. Avoid using the ladder in adverse weather conditions, and do not exceed the weight limit. Never use a ladder if you are feeling unwell or under the influence of drugs or alcohol.

• Introductory Physics Homework Help
Replies
20
Views
391
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
243
• Introductory Physics Homework Help
Replies
17
Views
676
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
2K