A plank inclined at an angle of α to the horizontal lies on two supports A and B (figure), over which it can slip without friction under the action of its own weight Mg. With what acceleration and in

Question

A plank inclined at an angle of α to the horizontal lies on two supports A and B (figure), over which it can slip without friction under the action of its own weight Mg. With what acceleration and in what direction should a man of mass m move along the plank so that it should not slip ?

TestHub · Accepted Answer

To balance the component of the plank's weight, men should move down the plank. In doing so, the friction exerted by the men on the plank will be in an upward direction, balancing the component of the plank's weight.

Now, drawing the Free Body Diagrams (FBDs) of the plank and the man:

$N = m g cos α . \dots\dots\dots (i)$

$f = m g sin α = ma \dots\dots\dots (ii)$

$f = M g sin α . \dots\dots\dots (iii)$

Balancing forces along the plank:

$f + m g sin α = ma$

$M g sin α + m g sin α = ma$

$g sin α [\frac{M}{m} + 1] = a$

$a = g sin α [1 + \frac{M}{m}]$

Options (A) and (B) are correct.

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Options:(select one or more)

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