Question
Download Solution PDFA 5 m long ladder is resting on a smooth vertical wall with its lower end 3 m from the wall. What should be the coefficient of friction between the ladder and the floor for equilibrium?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The resting on between any frictional floor and a vertical wall will always satisfy all the static equilibrium condition i.e.
∑ Fx = ∑ Fy = ∑ Mat any point = 0
Calculation:
Given:
Length of ladder (AB) = 5 m, OB = 3 m
Let W will be the weight of the ladder, NB and NA will be support reaction, θ is the angle between ladder and floor and μ is the friction coefficient between ladder and floor.
Free body diagram of the ladder;
OA2 = AB2 - OB2 , OA2 = 52 - 32
OA2 = 16, OA = 4 m
From Δ OAB,
\(\cos θ = \frac{3}{5}\)
Now apply ∑ Fy = 0
NB = W
Now take moment about point A, which should be equal to zero
∑ MA = 0
\(\;\left( {\mu {N_B} \times 4} \right) + \left( {W \times \frac{5}{2} \times \cos \theta } \right) = {N_B} \times 3\)
\(\;\left( {\mu {N_B} \times 4} \right) + \left( {{N_B} \times \frac{5}{2} \times \frac{3}{5}} \right) = {N_B} \times 3\)
\(\left( {\mu \times 4} \right) + \left( {\frac{3}{2}} \right) =~3\)
\(\mu = \frac{3}{8}\)
Hence the value of the coefficient of friction between ladder and floor will be 3/8
Last updated on May 30, 2025
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