Question

A small body A starts sliding down from the top of fixed wedge (as shown in the Figure) whose base is equal to l = 2.10 m. The coefficient of friction between the body and the wedge surface is k = 0.140. At what value of the angle α will the time of sliding be the least?

Answer 1

mg sin α – f = ma

f = µ mg cos α [\(\because\) µ N]

mg sin a – µ mg cos α = ma

∴ a = g sin α – mg cos α

a = g(sin α – µ cos α)

Now time taken by the block to reach point O;

Answer 2

\(\alpha = \frac{1}{2} tan^{-1}(\frac{1}{\mu})\)