# The Force Of The Ladder Against The Wall

• Coldry
In summary, the conversation is about calculating the force that a ladder is applying on a wall when a person is some way up the ladder. The parameters needed for the calculation are the length of the ladder, the angle at which the ladder is leaning, the weight of the ladder, the weight of the person, and the height of the person on the ladder. The person asking the question is unfamiliar with the math involved and is looking for a simplified explanation and visual aid. The person responding suggests looking at an introductory reference and creating a sketch to better understand the equilibrium of forces and torques involved in the calculation.
Coldry
OK folks, I'm sure this will be easy for the brains in this forum, but I've always been curious as to how this is done. So if you have situation where you have a ladder leaning on a wall and a person is some way up the ladder. If you know the length of the ladder (3m), the angle the ladder is leaning (50 Degrees at the bottom inside the triangle made by the ladder the floor and the wall), the weight of the ladder (10 kg), the weight of the person (110kg) and exactly how high up the ladder the person is (2.5m), how would you calculate the force the ladder is applying on the wall at the top of the ladder?

So I've put some random numbers for parameters here. I don't understand or know the maths involved, so if you need to make some of these numbers different to simplify the explanation please go ahead. Drawings would be appreciated.Thanks

Hello @Coldry,

I can understand you feel unable to do the calculation, but I have little patience with
Coldry said:
Drawings would be appreciated.
because I have absolutely no idea why you can't come up with at least an initial sketch !

So post that (*) and then we'll talk about the necessary equilibrium of forces, as well as about the equilibrium of torques that is needed to solve this one.
By the way, is this homework ? Because in PF, this exercise definitely qualifies as such...

 (*) that will also show how realistic your random parameter values appear

##\ ##

Coldry said:
I don't understand or know the maths involved,
Have a look at this introductory reference to see if it helps:

And then draw a sketch of the ladder and floor and wall, and show where the forces and moments (torques) are acting on it. We can help better once you've skimmed the reference and show us your initial sketch. Thanks.

## 1. What is the force of the ladder against the wall?

The force of the ladder against the wall is the amount of pressure or weight that the ladder exerts on the wall when it is leaned against it. This force is dependent on the weight of the ladder, the angle at which it is leaning, and the coefficient of friction between the ladder and the wall.

## 2. How is the force of the ladder against the wall calculated?

The force of the ladder against the wall can be calculated using the formula F = mg(sinθ + μcosθ), where F is the force, m is the mass of the ladder, g is the acceleration due to gravity, θ is the angle at which the ladder is leaning, and μ is the coefficient of friction between the ladder and the wall.

## 3. What factors affect the force of the ladder against the wall?

The force of the ladder against the wall is affected by the weight of the ladder, the angle at which it is leaning, and the coefficient of friction between the ladder and the wall. Additionally, the surface of the wall and the material of the ladder can also impact the force.

## 4. Why is it important to consider the force of the ladder against the wall?

It is important to consider the force of the ladder against the wall because it determines the stability and safety of the ladder. If the force is too great, the ladder may slip or fall, causing injury to the user. By understanding and calculating the force, proper precautions can be taken to ensure safe ladder usage.

## 5. How can the force of the ladder against the wall be minimized?

The force of the ladder against the wall can be minimized by reducing the weight of the ladder, using a ladder with a larger base or wider rungs, and ensuring the surface of the wall and the material of the ladder have a high coefficient of friction. It is also important to make sure the ladder is placed at the correct angle to distribute the force evenly.

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