A man of mass 60 kg is pulling a mass M by an inextensible light rope passing through a smooth and massless pulley with 60^ to the horizontal.The Coefficient of friction between the man and the ground is 0.5.the maximum value of M that can be pulled by the man without slipping on the ground is approximately




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Draw the free body diagram for the man.  see diagram.
     Ф = 60°
     T = M g
     N + T SinФ = m g    =>  N = mg - T SinФ = m g - M g SinФ
     Ff = T Cos Ф  = M g CosФ
     we know Ff    <=  mu * N     for the person not to slip

         M g Cos Ф <=  mu m g - mu M g Sin Ф
             M <=  mu m  /[ cos Ф + mu  SinФ ]
                 <=  0.50 * 60 / [ 1/2 + 0.50 * √3/2 ]   kg

         Mass M maximum value = 12.99 kg
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Mind blowing answer sir......awsum