Deriving an equation through a free body diagram

AI Thread Summary
To derive the equation Tanθ = static friction on an incline plane, a free body diagram is essential for visualizing the forces at play. The relationship between the force of friction and the normal force is expressed through the coefficient of friction. The angle θ is crucial as it relates to the tangent of the forces involved. It is important to note that the frictional force can be less than its maximum value, leading to the inequality tan(θ) ≤ μ_s, where μ_s represents the coefficient of static friction. Understanding these concepts is key to solving problems involving inclined planes and static friction.
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Homework Statement


Use a Free body diagram to show that :Tanθ=static friction, on an incline plane


Homework Equations



FF/FN= coeficiant of friction

The Attempt at a Solution


I know I must get an angle to have a tan of the Force of friction and a Normal force, but I don't understant why i need the the angle
 
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You should draw out the free body diagram (since that's what the question asks) and that's usually the best way to go about solving these kinds of questions anyway.

What was the actual question? It would make more sense if it asked you to show that:
tan(\theta) \leq \mu_s
(where \mu_s is the coefficient of static friction). And remember that the friction force can be less than its maximum possible value, which is why there is an inequality sign.
 
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