Determine couple - homogeneous cylinder, Mechanical Engineering

Determine couple - Homogeneous cylinder:

Homogeneous cylinder having weight W rests on horizontal floor in contact with wall (Figure given below). If the coefficient of friction for the all contact surfaces be µ, determine couple M acting on cylinder, which will begin counter clockwise rotation.

827_Homogeneous cylinder.png

Sol.: ∑H = 0 R1  - µR2 = 0

R1 = µR2                                                                                                                         ...(i)

∑V = 0  => R2  + µR1 = W                                                                                               ...(ii)

Putting value of R1 in equation (ii), we get

R2  + µ2R2 = W

R2 = W/(1 + µ2)                                                                                                                   ...(ii)

Putting value of R2 in equation (i), we get

R1 = µW/(1 + µ2)                                                                                                               ...(iv)

Taking the moment about O, we get

MO = µR1r + µR2r

= µr{R1 + R2}

= µr{(µW/(1 + µ2)) + (W/(1 + µ2))} = µrW{(1 + µ)/(1 + µ2)}

MO = µrW(1 + µ)/(1 + µ2)                                          .......ANS

 

Posted Date: 10/17/2012 6:53:00 AM | Location : United States







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