184_Dynamics 11ed Manual

184_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 13 determine the distance both blocks slide on the smooth surface before they begin to separate. What is their velocity at this instant? Solution: Block A: −k( x − d) − N = mA aA Block B: N = mB aB Since a A = aB = a, a= N= k( d − x) mA + mB kmB ( d − x) mA + mB Separation occurs when N=0 or x=d d v ⌠ k( d − x) ⌠ ⎮ v dv = ⎮ dx ⌡0 ⎮ mA + mB ⌡0 2⎞ ⎛ v k d ⎜d d − = mA + mB ⎝ 2 2 2 ⎟ ⎠ 2 v= kd mA + mB Problem 13-50 Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B , having a mass mB is pressed against A so that the spring deforms a distance d, show that for separation to occur it is necessary that d > 2μk g(mA+mB)/k, where μk is the coefficient of kinetic friction between the blocks and the ground. Also, what is the distance the blocks slide on the surface before they separate? Solution: Block A: −k( x − d) − N − μ k mA g = mA aA Block B: N − μ k mB g = mB aB 182 ...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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