or the plank not to slip, the man's legs should exert a force along it which balances the component of the force of gravity of the plank, i.e., which equals Mg sin α, and which is directed upwards. The plank will then exert an equal and opposite force on the man, i.e, Mg sin α, acting downwards along the plank. Besides this, the man is subject to the component of his own weight mg sin α. Consequently the man must move down the length of the plank with an acceleration relative to the earth such that
ma = Mg sin α + mg sin α,
hence
a = g sin α (1 + M/m).
-104 SOLUTIONS