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
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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