A small body A starts sliding down from the top of a wedge (Fig.) whose base is equal to λ = 2.10 m. The coefficient of friction between the body and the wedge-surface is k = 0.140. At what value of the angle will the time of sliding be the least? What will it be equal to?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
tan2 α = (–1 / k), α = 49º, t min = 1.0s
Sol. The acceleration of block is
w = 
or w = g sin α – kg cos α
Let AB = s ∴ cos α = 
∴ s = λ sec α
∴ According to kinematics equation
s = 
wt 2
∴ t = 
= 
or t 2 = 
= 
For being t minimum
sin α cos α – k cos 2 α is maximum
(sin α cos α – k cos 2 α ) = 0
cos 2 α – sin 2 α + 2k cos α sin α = 0
cos 2 α + k sin 2 α = 0
tan 2 α = 
⇒ α = 
tan –1 
After putting the values, α = 49º
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