Coefficient of static friction of uniform rod

In summary, a uniform rod with length l and weight W0 is connected to a rough wall at end A. A massless cord connects end B and is fixed to the wall at point C, forming an angle θ. To achieve static equilibrium, the minimum coefficient of static friction between the rod and the wall is μ≥tanθ. If a block with weight W=W0/2 is hung on the rod at a distance d from end A, the minimum coefficient of static friction is μ≥(2l-d)tanθ/(l+d). The pivot is set at end A and the torque equation should have a minus sign instead of a plus sign.
  • #1
maurice2705
6
0

Homework Statement


A uniform rod AB has a length l and a weight W0. End A is in contact with a rough wall, but it is not fixed. A massless cord connects end B and is fixed to the wall at point C. The rod AB is now horizontal and the angle formed between the cord and rod is θ as shown in the figure. (a) In order to achieve static equilibrium, what is the minimum value of the coefficient of static friction between the rod and the wall? (b) If a block of weight W=W0/2 is hang on the rod with the hanging point a distance d from the end point A, what is then the minimum value of the coefficient of static friction between the rod and the wall? Express all your results in terms of l, d, W0, and θ. (ANS: μ≥tanθ ; μ≥(2l-d)tanθ/(l+d) )


Homework Equations


Which point should we regard as the pivot?


The Attempt at a Solution


Set A as the pivot, then
Tsinθ+μN=W0
Tcosθ=N
Tsinθ*l+W0*l/2=0
Then I get μ=-3tanθ. What's wrong?
 
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  • #2
maurice2705 said:
... Tsinθ*l+W0*l/2=0
...What's wrong?

All correct except the + in the torque equation.
Try replacing the + by -.
 
  • #3
Thank you! I'd try again
 

Related to Coefficient of static friction of uniform rod

What is the coefficient of static friction?

The coefficient of static friction is a measure of the amount of force required to overcome the static frictional force between two surfaces in contact. It is typically denoted by the symbol μ and is a dimensionless quantity.

How is the coefficient of static friction determined?

The coefficient of static friction can be determined experimentally by measuring the maximum force required to move an object on a surface, divided by the vertical force acting on the object. It can also be calculated using the formula μ = F/mg, where F is the maximum force, m is the mass of the object, and g is the acceleration due to gravity.

What factors affect the coefficient of static friction?

The coefficient of static friction is affected by the nature of the two surfaces in contact, their roughness, and the amount of force pressing them together. It is also dependent on the presence of any intermolecular forces between the surfaces, which can vary depending on the materials involved.

How does the coefficient of static friction differ from the coefficient of kinetic friction?

The coefficient of static friction refers to the maximum amount of force required to overcome the static frictional force and initiate motion between two surfaces. The coefficient of kinetic friction, on the other hand, refers to the amount of force required to maintain motion between two surfaces that are already in motion.

What are some real-life applications of the coefficient of static friction?

The coefficient of static friction is important in many everyday activities, such as walking or driving a car. It is also crucial in engineering and construction, as it helps determine the stability and safety of structures and the materials used in them. Additionally, the coefficient of static friction is used in sports equipment, such as the grip on a tennis racket or the traction of a shoe on a surface.

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