Finding a friction force (ladder leaning against a wall )

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SUMMARY

The discussion centers on calculating the friction force acting on a ladder leaning against a wall, specifically when the coefficient of friction is 1.5 times a given value. Participants emphasize the relationship between static friction and the normal force (N_1), asserting that the friction force equals 1.5 times N_1 based on Newton's second law. The minimum friction force required to prevent slipping is expressed mathematically as cot(theta) * (Lgm_2 + M_1gd - 0.5m_dLg * (Lgm_1 + Lgm_2)^-1).

PREREQUISITES
  • Understanding of static friction and its relationship to normal force
  • Familiarity with Newton's second law of motion
  • Knowledge of trigonometric functions, specifically cotangent
  • Basic principles of mechanics involving forces and equilibrium
NEXT STEPS
  • Calculate friction forces in various scenarios using different coefficients of friction
  • Explore the application of Newton's second law in static equilibrium problems
  • Study the role of angles in friction calculations, particularly cotangent
  • Investigate real-world applications of friction in engineering and physics
USEFUL FOR

Students in physics or engineering courses, particularly those studying mechanics, as well as educators and professionals involved in force analysis and static equilibrium problems.

Linus Pauling
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1.
MTS_st_0.jpg


Suppose that the actual coefficient of friction is one and a half times as large as the value of . That is, . Under these circumstances, what is the magnitude of the force of friction that the floor applies to the ladder?
Express your answer in terms of , , , , , and . Remember to pay attention to the relation of force and .




2. static friction = magnitude of force in x direction, opposite sign



3. Ok, I had two exams today and I just almost went crazy calculating the the minimum friction force so that this ladder won't slip (brutal, but I did it). I am burnt out. How do I calculate N_1 here? It's the only force in the x direction other than friction, right? So by Newton's 2nd law the answer should just be friction = 1.5N_1, right?
 
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Could you please tell me wha t are the know data.
 
... that picture has everything except that calculated minimum friction force, which is:

cot(theta) * (Lgm_2 + M_1gd - 0.5m_dLg * (Lgm_1 + Lgm_2)^-1
 

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