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Lecture08_Coulomb_Friction_092710

# Lecture08_Coulomb_Friction_092710 - EAS 208(Fall 2010...

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EAS 208 (Fall 2010) Coulomb Friction Assume the block A shown in the Figure below. The block is resting on the surface, and the coefficient of static friction between the block A and the surface is s μ . In addition, an external force is applied on block ext F A . The F.B.D. (free body diagram) of block A is shown in the Figure below:

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From the F.B.D. of block , applying Newton’s second law in each direction ( A x y direction) we obtain the equations of motion for block : A x A x A A ext A A F m a m X F f m X Σ = = = && && (1) y A y A A A A F m a m Y N m g m Y Σ = = = && && A f (2) If we assume that block is stationary then the equations of motion become (from Eq. 1 and Eq. 2): A 0 ext A A ext F f m X F = = = && (3) 0 A A A A N m g m Y N m g = = = && (4) We can study two limiting cases. CASE A Assume that the external force is zero. From Eq. 3: ext F 0 ext F f f = = (5) Therefore, if there is no external force, from equilibrium the friction force is . 0 f = CASE B The maximum value that the static friction can take before block slides on the surface is given by the relation: A max s s f f N μ = = (6)
The normal force from Eq. 4 is
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Lecture08_Coulomb_Friction_092710 - EAS 208(Fall 2010...

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