Question

A wooden raft has a density of 300 kg/m^{3}. It has an
area of 12 m^{2} and is 1 m thick. Assuming that the
average mass of a person is 75 kg, how many people can this raft
hold if the raft floats in salty water with density of 1029
kg/m^{3}?

Answer #1

Area of wooden craft = 12m2

Thickness of wooden raft = 1m

Volume of wooden raft = 12×1

= 12m3

Density of wooden raft = 300kg/m3

Mass of wooden raft = 300kg/m3×12m3

= 3600kg

The wooden raft could float on water till the force exerted on water due to the weight of the raft and the people standing on it equals the weight of water displaced by the raft.

Weight of water displaced by raft,

W = 12m2×1029kg/m3m3×9.81m/s2

= 121133.88 N

Weight of the raft = 3600kg×9.81m/s2

= 35316 N

Weight of people in the raft = Weight of water displaced by raft - Weight of the raft

= 85817.88 N

Weight of a person = 75kg×9.81m/s2

= 735.75N

Total number of people =

= Total weight of people in raft/Weight of a person

= 85817.88/735.75

= 116.74

≈ 116

The raft can carry 116 people.

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