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 ?What percent of the logs is under water when you are on your raft in the water with your friend?
Please type entire problem.
Without knowing the density of the logs or the mass of you and your friend, no way.
call log density rho
call g = 9.81 m/s^2
water density = 1000 kg/m^2
mass of passengers = m
n = number of logs
n * .13^2 *2.2 = V, needed volume of logs
1000 g V = B = buoyancy force of logs fully submerged
floats when
B = m + rho g V
Density of logs is 600 kg/m^3 and weight is 512N for each
To determine the number of logs needed to build the raft, we'll first calculate the perimeter of the raft base using the average diameter of the logs. Then, we'll divide the perimeter by the length of each log to find the number of logs required.
1. Calculate the circumference of each log:
Circumference = π * Diameter
= 3.14 * 26cm
≈ 81.64cm
2. Calculate the total perimeter of the raft base:
Perimeter = 2 × (Length + Width)
= 2 × (2.2m + 2.2m)
= 2 × 4.4m
= 8.8m
3. Convert the perimeter to centimeters:
Perimeter = 8.8m × 100cm/m
= 880cm
4. Determine the number of logs needed:
Number of logs = Perimeter / Circumference
= 880cm / 81.64cm
≈ 10.77
Since we cannot have fractional logs, we will round up to the nearest whole number. Thus, we need a minimum of 11 logs to build the raft.
To calculate the percentage of the logs that will be underwater when you and your friend are on the raft, we'll use the principle of Archimedes' buoyancy.
1. Calculate the volume of each log:
Volume = π * (Radius^2) * Length
= 3.14 * (13cm)^2 * 220cm
≈ 99993.68cm³
2. Calculate the total volume of all logs:
Total Volume = Number of logs * Volume of each log
= 11 * 99993.68cm³
≈ 1099920.48cm³
3. Calculate the volume of water displaced by the combined weight of you and your friend (assuming an average weight of 70kg per person):
Volume of water = Total Weight / Density of water
= (2 × 70kg) / 1000kg/m³
= 0.14m³
= 140,000cm³
4. Calculate the percentage of the logs underwater:
Percentage of logs underwater = (Volume of water / Total Volume) * 100
= (140,000cm³ / 1099920.48cm³) * 100
≈ 12.73%
So, approximately 12.73% of the logs will be underwater when you and your friend are on the raft in the water.