A 4-meter plank weighing 8 kg is lying on a dock with 3.58 meters of its length on the dock, and the rest of its length extending off the dock. If a child weighing 57.2 kg walks out onto the part of the plank extending off the dock, what is the maximum distance in meters that the child can walk on the plank from the edge of the dock before he falls into the water

From the edge of the  dock this distance is 0.221 m

Explanation:

Length of the plank = 4 m

mass of the plank = 8 kg

mass of the child = 57.2 kg

We will assume that:

This means that the moment of the mass of the plank acts at (3.58 - 2 = 1.58 m) from the balance point.

For the maximum point the boy can walk while still maintaining stability, we balance the moment due to the mass of the plank against the moment that will be generated due to the mass of the boy, at the maximum distance at which stability is possible.

moment of the mass of the plank about the 3.58 m mark is

==> 8 x 1.58 = 12.64 kg-m

moment of the boy about  the 3.58 m mark is

==> 57.2 x d = 57.2d

where d is the maximum point at which stability is still possible

equating the two moments,

12.64 = 57.2d

d = 12.64/57.2 = 0.221 m away from the 3.58 m mark

the maximum distance at which stability is still possible is the maximum distance that the boy can walks before he falls into the water.

From the edge of the  dock this distance is 0.221 m

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