Prism 1 with bar 2 of mass m placed on it gets a horizontal acceleration a 0 directed to the left (figure). At what maximum value of this acceleration will the bar be still stationary relative to the prism, if the coefficient of friction between them k < cot α?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
w max = g (1 + k cot α ) / (cot α –k)
Sol.
(a 0 is acceleration of the wedge leftward)
As a 0 increases the component of ma 0 up the up the incline increases and friction attains its max value.
Writing the force equation along the incline and perpendicular to the incline.
ma 0 cos α – mg sin α – kN = 0.......(i)
mg cos α + ma 0 sin α = N .......(ii)
From equation (i) and (ii),
a 0 cos α – g sin α = kg cos α + K a 0 sin α
a 0 (cos α – k sin α ) = g {k cos α + sin α }
a 0 = 
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