Cofficient of static friction between table and rope

In summary, the coefficient of static friction between a table and rope is a measure of the force needed to start sliding the rope on the table. It is affected by factors such as the materials of the table and rope, the weight of the rope, and the surface properties of the table. A higher coefficient of static friction indicates a greater resistance to motion, while a lower coefficient suggests a smoother interaction between the two surfaces. This coefficient is an important consideration in various applications, such as rock climbing, where the friction between the rope and the surface is crucial for safety and stability.
  • #1
Mitchlan
4
0

Homework Statement



If the coefficient of static friction between an table and a uniform massive rope is [tex]\mu what fraction of the rope can hang over the edge of the table without the rope sliding?



b]2. Homework Equations [/b]



The Attempt at a Solution



Frictional force keeping it on the table: F[f] = mu (1-f) x m x g

Gravity pulling it off the table: F[g]= f x m x g

then: f x m x g = mu (1-f) x m x g

f= mu - mu x f

therefore the fraction of rope is f = mu / (1 + mu)


Thanks in advance!
 
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  • #3
Thanks for replying so soon. I did a quick search and couldn't find what I was looking for.
 
  • #4
Use google modifiers to search physicsforums. if you want to search the phrase
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  • #5


I would like to commend you for your attempt at solving this problem. Your approach is correct, and your final equation for the fraction of rope is also correct. However, I would like to point out that the coefficient of static friction, μ, is a dimensionless quantity and should not have the unit of [tex]\frac{m}{s}[/tex]. Also, the symbol "f" is usually used for the force of friction, so it might be less confusing to use a different variable for the fraction of rope, such as "x". Keep up the good work!
 

Related to Cofficient of static friction between table and rope

1. What is the coefficient of static friction between a table and a rope?

The coefficient of static friction is a measure of the resistance between two surfaces that are not moving relative to each other. In the case of a table and a rope, it refers to the amount of force required to keep the rope from sliding across the table.

2. How is the coefficient of static friction calculated?

The coefficient of static friction is calculated by dividing the maximum force of friction between two surfaces by the normal force pressing the surfaces together. This ratio is denoted as μs and is a unitless value.

3. What factors affect the coefficient of static friction between a table and a rope?

The coefficient of static friction can be influenced by several factors including the materials of the surfaces, the roughness of the surfaces, and the presence of any lubricants or contaminants.

4. What is the typical range of values for the coefficient of static friction?

The coefficient of static friction can vary greatly depending on the materials of the surfaces in contact. However, in general, it falls within the range of 0.1 to 1.0, with 1.0 representing the highest possible friction between two surfaces.

5. Why is the coefficient of static friction important in the context of a table and a rope?

The coefficient of static friction is important in this context because it determines the minimum force required to keep the rope from sliding across the table. This information is crucial for ensuring the stability and safety of objects placed on the table, as well as for designing structures that will support the weight of the rope without slipping.

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