Static friction and fraction of mass of rope that can hang.

In summary, the coefficient of static friction between a rope and a table determines the maximum fraction of the rope that can hang over the edge of the table before it begins to slip. This can be expressed in terms of μ, the coefficient of static friction, but it may require breaking down the equations and using x and y components. It is important to show your work in order to fully understand the reasoning behind the answer.
  • #1
chiuda
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Homework Statement



The coefficient of static friction between a rope and the table on which it rests is μ.
Find the fraction of the rope that can hang over the edge of the table before it begins to slip.
Express your answer in terms of μ.


Homework Equations





The Attempt at a Solution



i have tried to break all the equations i know into their parts like x and y components using just variables since no numbers are given but i just can't seem to isolate for something multiplied to μ. For some reason i think it is just μ but i do not truly understand why this would be if anyone could help it would be really appreciated as it is the last question in an online assignment and i have been working at it for quite some time. Thanks in advance.
 
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  • #2
Show your work.
 

Related to Static friction and fraction of mass of rope that can hang.

1. What is static friction?

Static friction is the force that resists the motion of an object on a surface when there is no relative motion between the two. It is caused by the interlocking of microscopic bumps and valleys on the surface of the object and the surface it is resting on.

2. How is static friction different from kinetic friction?

Static friction acts to prevent the start of motion, while kinetic friction acts to slow down an object that is already in motion. Static friction is generally greater than kinetic friction, making it more difficult to overcome.

3. What factors affect the amount of static friction?

The amount of static friction depends on the roughness of the surfaces in contact, the normal force (the force pushing the surfaces together), and the materials involved.

4. How is the fraction of mass of rope that can hang calculated?

The fraction of mass of rope that can hang is calculated by dividing the maximum static friction force by the force of gravity acting on the object. This will give you a decimal value, which can be converted to a percentage by multiplying by 100.

5. Can the fraction of mass of rope that can hang vary for different types of rope?

Yes, the fraction of mass of rope that can hang can vary depending on the material and thickness of the rope. Thicker and stronger ropes will have a higher fraction of mass that they can support compared to thinner and weaker ropes.

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