Question

A raft is made of 11 logs lashed together. Each is 34.0 cm in diameter and has a length of 5.50 m. How many people (whole number) can the raft hold before they start getting their feet wet, assuming the average person has a mass of 69.0 kg? Do not neglect the weight of the logs. Assume the density of wood is 600 kg/m³

Answer 1

Here the forces that act on the logs + people system would be their weight and the other force will be the buoyant force which arises due to volume immersed in water.

Vertical forces acting on the logs+people system are

(1) Weight of the people + weight of the logs acting vertically downwards

...............................................................(1)

Where is the number of people. And is the weight of each person.

is the radius of each log and is the length of each log

is the density of wood (logs)

is the acceleration due to gravity.

(2) the buoyant force acting vertically upwards

Since they want the maximum number of people without just their feet wet, we can say that the entire volume of the logs is just immersed.

According to Archimedes' principle,

where,

is the Buoyant force

is the density of water (the fluid that is being displaced)

is the volume of part of the body that is immersed in the liquid, which is also the volume of the fluid displaced

is the acceleration due to gravity.

...............................................................(2)

So the given condition is that this logs+people system should float, that is, not sink. Therefore at the surface they are in equilibrium in the vertical direction.

i.e.,

.............................................(3)

Substituting (1) and (2) in (3) we get.

Substituting all known values into the above equation, we can solve for  .

We get

Since is number of people it can't take a fractional value like 31.2.

So the maximum number of people is 31.