Question

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

Answer 1

Let T be the maximum force exerted by the man on the rope.

From the free body diagram,
R + T = Mg
⇒ R = Mg − T                     (1)
Again,
R₁ − R − mg = 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

`=> "T" = (mu  ("M"+"m")"g")/(1+mu)`

Therefore, the maximum force exerted by the man is `(mu  ("M"+"m")"g")/(1+mu)`.