Finding a friction force (ladder leaning against a wall )

AI Thread Summary
The discussion focuses 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 highlight the relationship between static friction and the forces acting in the x-direction, emphasizing that friction must balance the horizontal forces. One user expresses frustration after exams but seeks clarification on calculating the normal force (N_1) and its relation to friction, suggesting that friction equals 1.5 times N_1 based on Newton's second law. The minimum friction force is also discussed, with a formula provided that incorporates various parameters like angles and masses. Understanding these calculations is crucial for determining the stability of the ladder.
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Suppose that the actual coefficent 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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