Question

Whatever floats your boat

You and your two friends Tom Sawyer and Huck Finn each weigh 70 kg and want to build a raft out of

logs to float from Hope to Vancouver on the Fraser River. The Birch logs that you have found are 3.0 m

long, 0.5 m diameter and have a specific density of 0.70. You want to know how many logs you need to

use to build your raft so that you all keep your feet dry.

Answer 1

Total weight of the logs + weight of 3 persons = Buoyant force
n x _L x V_L x g + 3 x m x g = n x _W x V_L x g          ...(1)
Where n is the number of logs, _L is the density of logs, V_L is the volume of logs, m is the mass of each person, _W is the density of water and g is the acceleration due to gravity.

n x _L x V_L + 3 x m = n x _W x V_L         [Cancelling g from (1)]
n V_L x [_W - _L] = 3m
n = 3m / [V_L x [_W - _L]]                    ..(2)
V_L = 3 x x (0.25)²
= 0.589 m³
Substituting in (2),
n = (3 x 70) / [0.589 x [1 x 10³ - 0.7 x 10³]
= 210/176
= 1.2
At least 2 logs are needed.