Raft made of 2.2m long pine logs.Average diameter of logs 26cm.How many logs are needed to strap together to build raft to hold max 4 people?
What percent of the logs is under water when you are on your raft in the water with your friend?
To calculate the number of logs needed to build a raft to hold a maximum of 4 people, we need to determine the length required for the raft.
Assuming we arrange the logs side by side, the length of the raft would be equal to the combined length of the logs. Therefore, we need to calculate how many logs are needed to reach a length of at least 2.2 meters.
Since the average diameter of the logs is given as 26 cm, we can use this information to calculate the circumference of each log, which will help us determine how many logs are needed.
The circumference of a circle (which represents the cross-section of the logs) can be calculated using the following formula:
Circumference = π * diameter
Where π is approximately equal to 3.14.
For the average diameter of 26 cm,
Circumference = 3.14 * 26 cm
Circumference = 81.64 cm
To find the number of logs needed, we can divide the total required length (2.2 meters or 220 cm) by the circumference of each log.
Number of logs needed = Total required length / Circumference of each log
Number of logs needed = 220 cm / 81.64 cm
Number of logs needed ≈ 2.696
Since we can't have a fraction of a log, we would need to round up the number of logs to the nearest whole number.
Therefore, we would need a minimum of 3 logs to build the raft.
To calculate the percentage of the logs that would be under water when 2 people are on the raft, we need to determine the weight supported by the logs.
Assuming the average weight of a person is 70 kg and two people would be on the raft:
Total weight supported by the raft = Weight of each person * Number of people
Total weight supported by the raft = 70 kg * 2
Total weight supported by the raft = 140 kg
To calculate the percentage of the logs under water, we need to relate the weight supported by the logs to the weight of the raft itself.
The weight of the raft can be determined by multiplying the density of pine logs by their volume.
Density of pine logs ≈ 480 kg/m³ (source: https://www.engineeringtoolbox.com/wood-density-d_40.html)
Volume of each log = π * (radius²) * length
Volume of each log = 3.14 * (13 cm)² * 220 cm (converted to cm for consistency)
Volume of each log ≈ 98214.4 cm³ (or 0.09 m³)
Total weight of the raft = Density of pine logs * Volume of each log
Total weight of the raft ≈ 480 kg/m³ * 0.09 m³
Total weight of the raft ≈ 43.2 kg
Now, we can calculate the percentage of the logs under water using the weight supported by the logs and the total weight of the raft.
Percentage of logs under water = (Weight supported by logs / Total weight of raft) * 100
Percentage of logs under water = (140 kg / 43.2 kg) * 100
Percentage of logs under water ≈ 324.07%
Therefore, when you and your friend are on the raft, approximately 324.07% of the logs would be under water.
To calculate the number of logs needed to build a raft to hold a maximum of 4 people, we first need to determine the dimensions of the raft. Assuming the logs are placed side by side and are tightly packed, the length of the raft would be the sum of the lengths of the logs. In this case, each log is 2.2m long, so the total length would be 2.2m multiplied by the number of logs.
To calculate the number of logs needed, we divide the length of the raft by the length of each log. Thus, the equation is:
Number of logs = Total length of raft / Length of each log
In this case, the total length of the raft is 2.2m multiplied by the number of logs, and the length of each log is 2.2m. Substituting these values into the equation, we get:
Number of logs = (2.2m * Number of logs) / 2.2m
To solve for the unknown variable, we can cross multiply:
Number of logs * 2.2m = 2.2m * Number of logs
This simplifies to:
Number of logs = (2.2m * Number of logs) / 2.2m
Now, we can cancel out the common factor of 2.2m on both sides of the equation:
Number of logs = Number of logs
Therefore, the equation is an identity, indicating that any number of logs can be used to build a raft.
Moving on to the second part of your question, let's calculate the percentage of the logs that are underwater when you and your friend are on the raft. Assuming the logs are cylindrical in shape, the fraction of the logs submerged in water would be proportional to the submerged volume relative to the total volume of the logs.
The total volume of a cylindrical log can be calculated using the formula:
Total Volume = π * (radius)^2 * height
In this case, the average diameter of the logs is given as 26cm. Diameter is twice the radius, so the radius of each log would be 26cm / 2 = 13cm = 0.13m. The height of each log is given as 2.2m.
The total volume of each log can be calculated by substituting these values into the formula:
Total Volume = π * (0.13m)^2 * 2.2m
Now, to find the volume of the submerged portion of the log, we need to determine the depth to which the logs are submerged. Let's assume that the logs are fully submerged and that their tops are just at the water level. In this case, the depth to which the logs are submerged would be equal to the radius of each log, which is 0.13m.
The submerged volume of each log can be calculated using the formula:
Submerged Volume = π * (radius)^2 * depth
Substituting the values into the formula, we get:
Submerged Volume = π * (0.13m)^2 * 0.13m
Now, let's calculate the percentage of the logs that are underwater by dividing the submerged volume by the total volume and multiplying by 100:
Percentage of logs underwater = (Submerged Volume / Total Volume) * 100
Substituting the values into the formula, we get:
Percentage of logs underwater = [(π * (0.13m)^2 * 0.13m) / (π * (0.13m)^2 * 2.2m)] * 100
Simplifying the equation further, we find:
Percentage of logs underwater = (0.13m / 2.2m) * 100
Calculating this expression, we get:
Percentage of logs underwater = (0.13 / 2.2) * 100 ≈ 5.9%
So, approximately 5.9% of the logs are underwater when you and your friend are on the raft in the water.