FrictionHard
Question
A plank is held at an angle a to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass m should move so that the plank does not move.
Options
A.g sin α 
down the incline
down the incline B.g sin α up the incline
up the incline C.g sin α 
down the incline
down the incline D.g sin α up the incline
up the incline Solution
For plank be at rest, applying Newton′s second law to plank along the incline
Mg sin α = f ....................................(1)
and applying Newton′s second law to man along the incline.
mg sin α + f = ma ....................................(2)
a = g sin α
down the inclineAlternate Solution :
If the friction force is taken up the incline on man, then application of Newton′s second law to man and plank along incline yields.
f + Mg sin α = 0 ..........(1)
mg sin α α f = ma ..........(2)
Solving (1) and (2)
a = g sin α
down the inclineAlternate Solution :
Application of Newton′s seconds law to system of man + plank along the incline yields
mg sin a + Mg sin a = ma
a = g sin α
down the inclineCreate a free account to view solution
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