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Mechanics 1G

# Mechanics 1G - 2.001 MECHANICS AND MATERIALS I Lecture#4...

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2.001 - MECHANICS AND MATERIALS I Lecture #4 9/18/2006 Prof. Carol Livermore TOPIC: FRICTION EXAMPLE: Box on ﬂoor μ s =Coeﬃcient of Static Friction FBD Equation of equilibrium F y = 0 N W = 0 N = W F x = 0 1

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T F = 0 T = F At impending motion only : F = μ s N For well lubricated, μ s 0 . 05. For very clean surfaces μ s 0 . 4 1. After it starts to move: F = μ k N μ k = Coeﬃcient of kinetic friction. μ k < μ s EXAMPLE: Block on an inclined plane Q: At what angle ( α ) does the block slide down the plane? FBD: 2
Equilibrium F x = 0 F W sin α = 0 F = W sin α F y = 0 N W cos α = 0 N = W cos α So: F = tan α N When you have impending motion: F = μ s N μ s = tan α What about where these forces act? M 0 = 0 FL 2 N a = 0 2 FL 2 L 2 a = = tan α 2 N 2 So:

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So: L 2 a = tan α 2 The resultant of the normal force and frictional force act directly ”below” the center of mass. EXAMPLE Q: For what range of W 0 is the block in equilibrium?
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Mechanics 1G - 2.001 MECHANICS AND MATERIALS I Lecture#4...

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