The friction coefficient between the board and the floor shown in figure (6-E7) is μ. Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.



From the free body diagram,
R + T = Mg
R = MgT (1)
Also,
R1 Rmg = 0
R1 = R + mg (2)
and
T μR1 = 0


From Equation (2),
T − μ(R + mg) = 0
T − μR − μ mg = 0
T − μ(Mg − T) − μmg = 0
T − μMg + μt − μmg = 0


T (1 + μ) = μMg + μmg



Therefore, the maximum force exerted by the man is


1