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..Concept of Physics - 1 , HC VERMA , Chapter 6:Friction "
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Solution :
Let the maximum force exerted by the man is T.
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 (ii), T-μ(R+mg)=0
T-μ(Mg +T) -μmg=0
T(1+μ)=μMg+μmg=0
T(1+μ)=μ(M+m)g
T=μ(M+m)g/1+μ
Maximum Fore exerted by man is μ(M+m)g/1+μ
Let the maximum force exerted by the man is T.
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 (ii), T-μ(R+mg)=0
T-μ(Mg +T) -μmg=0
T(1+μ)=μMg+μmg=0
T(1+μ)=μ(M+m)g
T=μ(M+m)g/1+μ
Maximum Fore exerted by man is μ(M+m)g/1+μ
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