Coefficient of Friction between Floor and Ladder

In summary: So, in summary, to find the minimum coefficient of friction between the floor and the ladder, we used the concept of torque and set up an equation to find the friction force. From there, we were able to solve for the coefficient of friction. I hope this helps clarify the problem for you!
  • #1
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Homework Statement



A uniform 5.0m long ladder leans against a friction-less wall making an angle of 22 degrees with the floor. The ladder has a mass of 42kg and a 67kg painter stands 3.5m up the ladder.

A) Find the minimum coefficient of friction between the floor and the ladder.

Homework Equations



Painter: 9.8kg/N * 67kg = 656.6N
Ladder: 9.8kg/N * 42kg = 411.6N

The Attempt at a Solution



nb670o.jpg


[(3.5m)(cos 22)(656.6N)] + [(2.5m)(cos 22)(411.6N)] = Ff = 3085N

[(3.5m)(sin 22)(656.6N)] + [(2.5m)(sin 22)(411.6N)] = Fn = 1246N

mu = 3085N/1246N = 2.476


The above attempt was basically a cry of desperation because I am very confused by this problem. My class has done some vectors and kinematics last year but I am new to this so this is still quite confusing to me.

I'd just like to know how to go about doing this correctly. I don't want someone to give me the direct answer but to guide in the correct direction towards getting the answer would be great. Thanks in advance.

Also, I'm going to assume right now that the above "FBD" that I've drawn is set up wrong in at least some way. Just saying that the diagram is my interpretation of the question and that the diagram isn't actually given in the question.
 
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  • #2


Hi there,

First of all, great attempt at solving the problem! It's clear that you have a good understanding of the forces involved and how to set up a free body diagram.

To solve this problem, we need to use the concept of torque, which is the rotational equivalent of force. In this case, we are looking at the torque on the ladder caused by the painter's weight and the weight of the ladder itself.

The formula for torque is: torque = force x distance x sin(angle), where the angle is the angle between the force and the lever arm (the distance from the pivot point to the point where the force is applied).

In this case, the pivot point is the point where the ladder touches the ground and the force is the weight of the ladder and the painter. The distance from the pivot point to the weight of the ladder is 2.5m and the distance from the pivot point to the weight of the painter is 3.5m.

So, the torque due to the ladder is: torque = (411.6N)(2.5m)sin(22) = 989.4N*m

And the torque due to the painter is: torque = (656.6N)(3.5m)sin(22) = 1566.6N*m

Now, we need to consider the torque due to the friction force. The friction force acts in the opposite direction of the motion, so it will cause a torque in the opposite direction of the weight of the ladder and the painter.

The distance from the pivot point to the point where the friction force acts is the length of the ladder, 5.0m. So, the torque due to friction is: torque = (Ff)(5.0m)sin(22) = 5Ff

Now, we can set up an equation to find the minimum coefficient of friction:

989.4N*m + 1566.6N*m - 5Ff = 0

Solving for Ff, we get: Ff = (989.4N*m + 1566.6N*m)/5 = 511.2N

And finally, we can plug this value back into our original equation to find the minimum coefficient of friction:

mu = Ff/Fn = 511.2N/(1246N + 411.6N) = 0.
 

1. What is the coefficient of friction between a floor and a ladder?

The coefficient of friction between a floor and a ladder is a measure of the amount of resistance or friction that exists between the two surfaces. It is typically denoted by the symbol "μ" and is a dimensionless number that ranges from 0 to 1.

2. How is the coefficient of friction between a floor and a ladder determined?

The coefficient of friction between a floor and a ladder is determined through experiments and calculations. These experiments involve measuring the force required to move the ladder across the floor at different angles and then using this data to calculate the coefficient of friction.

3. What factors affect the coefficient of friction between a floor and a ladder?

The coefficient of friction between a floor and a ladder can be affected by a variety of factors such as the type and condition of the floor surface, the weight and material of the ladder, and the angle at which the ladder is placed on the floor. Additionally, factors such as temperature, humidity, and surface contaminants can also impact the coefficient of friction.

4. Why is the coefficient of friction between a floor and a ladder important?

The coefficient of friction between a floor and a ladder is important for safety purposes. A low coefficient of friction means that there is less resistance between the surfaces, making it easier for the ladder to slip or slide. This can result in accidents and injuries. Therefore, it is important to know the coefficient of friction in order to ensure proper safety precautions are taken when using a ladder.

5. How can the coefficient of friction between a floor and a ladder be increased?

The coefficient of friction between a floor and a ladder can be increased by using materials that have a higher coefficient of friction, such as rubber or textured surfaces. Additionally, keeping the surfaces clean and dry can also help to increase the coefficient of friction. Placing anti-slip pads or grip tape on the ladder feet can also improve the friction between the ladder and the floor.

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