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I state here a problem from S.L.Loney : A plank of mass $M$ is initially at rest along a line of greatest slope of a smooth plane inclined at an angle $α$ to the horizon and a man of mass $M'$ starting from the upper end walks down the plank so that it does not move. To find the time taken by the man to reach the other end. Length of the plank is $a$.

My question is, if the plank doesn't move, what's the point of the problem? How is it any different from a simple kinematics problem? I know it is; just don't see why.

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If there was no person, the plank would slide down due to gravity,

But while person walks downwards, he pushes plank upwards,due to friction,

The forces due to gravitation and man cancel out,

So the plank doesn't move,

Now we need to calculate the velocity/acceleration of man for which the plank does not move.

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  • $\begingroup$ No the plank doesn't slide back, it's the man who keeps it from sliding down. You need to calculate velocity of man for which the gravitational force and his force on the plank are equal. $\endgroup$ – neonpokharkar Sep 15 '17 at 19:13
  • $\begingroup$ Oh okay. So it IS a regular problem only I need to find the particular velocity and acceleration of the man for which the plank stays still? $\endgroup$ – Hrit Roy Sep 15 '17 at 19:14
  • $\begingroup$ Yes it is a regular problem $\endgroup$ – neonpokharkar Sep 15 '17 at 19:14
  • $\begingroup$ I had deleted my previous comment as soon as I realized it. Thanks :) $\endgroup$ – Hrit Roy Sep 15 '17 at 19:15
  • $\begingroup$ You're welcome ;) $\endgroup$ – neonpokharkar Sep 15 '17 at 19:15

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