Coefficient of static friction of uniform rod

Click For Summary
SUMMARY

The discussion focuses on calculating the minimum coefficient of static friction required for a uniform rod AB, with length l and weight W0, to achieve static equilibrium when positioned horizontally against a rough wall. The analysis involves a massless cord connecting end B to a wall at point C, forming an angle θ with the rod. The minimum coefficient of static friction is derived as μ≥tanθ for the initial scenario and μ≥(2l-d)tanθ/(l+d) when a block of weight W=W0/2 is added at a distance d from end A. The correct torque equation is crucial for accurate calculations.

PREREQUISITES
  • Understanding of static equilibrium principles
  • Knowledge of torque and forces in physics
  • Familiarity with the concept of coefficients of friction
  • Ability to manipulate trigonometric functions in equations
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn about torque calculations and their applications
  • Explore the concept of friction and its coefficients in detail
  • Investigate the effects of angles on forces in equilibrium scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and static equilibrium, as well as educators seeking to explain the concepts of friction and torque in practical applications.

maurice2705
Messages
6
Reaction score
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?
 
Physics news on Phys.org
maurice2705 said:
... Tsinθ*l+W0*l/2=0
...What's wrong?

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

Similar threads

  • · Replies 20 ·
Replies
20
Views
2K
Replies
13
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
Replies
4
Views
2K
  • · Replies 46 ·
2
Replies
46
Views
5K
  • · Replies 15 ·
Replies
15
Views
1K