Review Conceptual Example 7 before starting this problem. A uniform plank of len

Question

Review Conceptual Example 7 before starting this problem. A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 447 N walk on the overhanging part of the plank before it just begins to tip? x = A block (mass = 2.4 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.5 x 10^-3 kg. m^2), as the drawing shows. Initially the pulley is

Explanation / Answer

Weight distribution of plank = (225/5) = 45 N. per metre length.
So, the overhanging end weighs (1.1 x 45) = 49.5 N., and the rest weighs (225 - 49.5) = 175.5 N.
Taking the right support as the fulcrum, on the right there is 49.5 N. situated 1/2 the distance out from the fulcrum, = (49.5 x 0.55m) = 27.225 N/m torque.
On the left side, is 175.5N., situate 1/2 the distance from the fulcrum to the left end, which is 1.95 m.
(175.5 x 1.95) = 342.225 N/m. torque.
When a person weighing 447N. moves past the right support, the torque applied , including the 27.225N. already right of the fulcrum, must be equal to or less than the torque on the left end. (342.225 - 27.225) = max. 315 N/m can be created by the person's weight.
(315 /447) = maximum distance of 0.705 m. the person can be, past the right support.

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