A triangular wedge of mass M which is free to move, is at rest on smooth horizontal plane. A man of mass m initially at rest starts running over wedge with constant speed u relative to wedge. If we do analysis from ground while man is running without jumping, with constant speed over wedge, which of the following statements are wrong?

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The power due to normal contact force on the man is zero.

The friction force acting on the man is mg $\sin θ$ .

Power due to friction on the man is zero.

Power due to normal constant force on the wedge is positive.

answer is A, C, D.

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Detailed Solution

Along the incline, $a_{m} = 0$
$f_{s} = m g \sin α$ ___________(B)
By N, on man, $P_{m} = N' v' \sin α > 0$ ____________(A)
By ____________ $f_{s}, P_{w} + P_{m} = 0 \Rightarrow f_{s} v \cos α + p_{m} = 0 \Rightarrow p_{m} = - f_{s} v \cos α < 0$ (C)
On the wedge, angle between N and ‘v’ is $90 + α$
$P_{N} = N v \cos (π / 2 + α) < 0$ ______________(D)