Final answer:
The smallest number of whole logs needed to build a raft to carry four people is 10.
Step-by-step explanation:
To calculate the number of logs needed to build a raft that can carry four people, we need to determine the buoyant force required to keep the raft afloat. The buoyant force is equal to the weight of the people it needs to support. The weight of four people is 4 x 71.0 kg = 284.0 kg.
The buoyant force is given by the equation Fb = ρVg, where ρ is the density of water (1000 kg/m³), V is the volume of the logs, and g is the acceleration due to gravity (9.8 m/s²).
Calculating the Volume of the Logs:
The volume of a cylinder (which approximates the shape of a log) is given by the equation V = πr²h, where r is the radius of the log and h is the length of the log.
Plugging in the given values, we find that the volume of one log is V = π(0.0600 m)²(2.60 m) ≈ 0.0291 m³.
Calculating the Number of Logs:
Dividing the weight of the people by the buoyant force per log, we get the number of logs needed: 284.0 kg / (ρVg) ≈ 284.0 kg / (1000 kg/m³ * 0.0291 m³ * 9.8 m/s²) ≈ 10.0 logs.
Therefore, the smallest number of whole logs that can be used to build a raft to carry four people is 10.