What is the smallest number of whole logs (ñ = 725 kg/m3, radius = 0.0556 m, length = 3.80 m) that can be used to build a raft that will carry four people, each of whom has a mass of 73.0 kg?
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Research Analyst
Construction Management
To determine the smallest number of logs needed to build a raft, we need to calculate the buoyant force exerted by the logs and compare it to the total weight of the four people.
The buoyant force exerted by an object immersed in a fluid (in this case, water) can be calculated using Archimedes' principle:
Buoyant Force = Weight of the Fluid Displaced
Firstly, we need to determine the weight of the fluid displaced by a single log. The volume of a cylinder is given by the formula:
Volume = π * (radius^2) * height
Substituting the given values, we can calculate the volume of a single log:
Volume = π * (0.0556^2) * 3.80 m
Next, we can determine the weight of the fluid displaced by the log using the density of water:
Weight of the Fluid Displaced = Volume * Density of Water
Given that the density of water is 1000 kg/m^3, we can calculate the weight of the fluid displaced by a single log:
Weight of the Fluid Displaced = Volume * 1000 kg/m^3
Now, we can calculate the buoyant force exerted by a single log. The weight of the fluid displaced is equal to the buoyant force:
Buoyant Force = Weight of the Fluid Displaced
To check if the sum of buoyant forces exerted by a certain number of logs is greater than or equal to the total weight of the four people, we need to multiply the buoyant force of a single log by the number of logs.
Finally, we can calculate the smallest number of logs needed by dividing the total weight of the four people by the buoyant force of a single log and rounding up to the nearest whole number.
Please note that we are assuming that the logs are arranged in a way that evenly distributes the weight and provides stability for the raft.