Question

A heavy, 6 m long uniform plank has a mass of 30 kg. It is positioned so that 4 m is supported on the deck of a ship and 2 m sticks out over the water. It is held in place only by its own weight. You have a mass of 70 kg and walk the plank past the edge of the ship. How far past the edge do you get before the plank starts to tip, in m

Answer 1

Answer:

about 1 meter

Explanation:

   

Answer 2

The distance past the edge that the man will get before the plank starts to tip is; 0.4285 m

We are given;

Mass of plank; m = 30 kg

Length of plank; L = 6m

Mass of man; M = 70 kg

Since the plank has 2 supports which are the deck of the ship, then it means that, we can take moments about the right support before the 2m stick out of the plank.

Thus;

Moment of weight of plank about the right support;

τ_p = mg((L/2) - 2)

τ_p = 30 × 9.8((6/2) - 2)

τ_p = 294 N.m

Moment of weight of man about the right support;

τ_m = Mgx

where x is the distance past the edge the man will get before the plank starts to tip.

τ_m = 70 × 9.8x

τ_m = 686x

Now, moment of the board is counterclockwise while that of the man is clockwise. Thus;

τ_m = τ_p

686x = 294

x = 294/686

x = 0.4285 m

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