Two people weighing 'W' each are sitting on a plank of length 'L' floating on water at L/4 from either end, neglecting the weight of the plank the bending moment at center of plank is

Concept:

The given information in question can be represented in the given figure:

The water will exert uniform pressure at the bottom plank in the upward direction.

Calculation:

Given:

Since it is given that Plank is floating on water. We get,

Upward force (buoyant force) exerted by water = Downward weight of pressure standing on Plank

(W')(L) = 2W

\(W' = \frac{{2W }}{L}\)

Consider midsection (left) of plank,

Consider Moment at the midpoint to be zero.

∑ Mmid = 0

\({M_{mid}} + W \times \frac{L}{4} = \frac{{{W'}\times L}}{2} \times \frac{L}{4}\)

\({M_{mid}} + \frac{{W \times L}}{4} = \left( {\frac{{2\times W }}{L}}\right)\times \left ( {\frac{L}{2}} \right)\times \left( {\frac{L}{4}} \right)\)

∴ Mmid = 0