Consider a group of people trying to stay afloat after their boat strikes a log in a lake. Construct a problem in which you calculate the number of people that can cling to the log and keep their heads out of the water. Among the variables to be considered are the size and density of the log, and what is needed to keep a person’s head and arms above water without swimming or treading water.

Solution 86PE

The buoyant force applied by the water will be equal to the weight of the people’s submerged body and the weight of the log.

Step 1 of 4</p>

Let there are people.

Average density of human body kg/m3

Let the mass of each person be kg

Therefore, total weight of the people

Assume that 95% of each person’s body is submerged in water.

Therefore, the weight of the people submerged is

Step 2 of 4</p>

Let the density of the log material be 500 kg/m3. It is lower than the density of water and hence it is floats.

Let the length and radius of the log be 3.00 m and 30 cm respectively.

Therefore, its volume,

(30 cm)23.00 m

(0.30 m)23.00 m

m3

Therefore, the mass of the log is,

kg

kg

So, the weight of the log is,