A raft is made of 14 logs lashed together. Each is 62 cm in diameter and has a length of 7.5 m.
How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 67 kg ? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.69.
Physics Help. Answer please?
2015-12-09 9:10 pm
回答 (2)
2015-12-09 10:06 pm
✔ 最佳答案
The logs have a total volumeV = N*(π/4)d²*L = 14 * π/4 * (0.62m)² * 7.5m = 31.7 m³
and so will displace a total mass of water
M = ρ*V = 1000kg/m³ * 31.7m³ = 31 700 kg
The raft itself has mass
Mr = ρr*V = 0.69 * 1000kg/m³ * 31.7m³ = 21 873 kg,
so it can support a mass of people
Mp = M - Mr = 9827 kg
That's n = 9827kg / 67kg/person = 146 people
(rounded down).
Hope this helps!
2015-12-09 10:31 pm
The specific gravity is the ratio of the density of a log to the density of water. The density of water is 1000 kg/m^3.
For a log, density = 690 kg/m^3
For the raft to float, the buoyant force must be equal or greater than the total weight. Let’s use the following equation to determine the volume of a log in m^3.
Volume = π * r^2 * L, r = 0.31 m
Volume = π * 0.31^2 * 7.5 = π * 0.72075
This is approximately 2.264 m^3.
Let’s use the following equation to determine the mass of the raft.
Mass = Volume * density = π * 0.72075* 690 = π * 497.3175 kg
Weight = 9.8 * π * 497.3175 = π * 4873.7115 N
This is approximately 15,311N.
Buoyant force = Density of water * g * Volume of boat
Buoyant force = 1000 * 9.8 * π * 0.72075 = π * 7063.35
This is approximately 22,190 N. To determine the weight of the people, subtract the weight of the raft from the buoyant force.
Weight = π * 7063.35 – π * 4873.7115 = π * 2189.6385
This is approximately 6880 N.
Weight of one person = 67 * 9.8 = 656.6 N
Number of people = π * 2189.6385 ÷ 656.6
This is approximately 10.5 people. So, 10 people is the answer.
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OR
To determine the fraction of the raft that is above water before the people get on it, subtract the specific gravity of the raft from the specific gravity of water.
1 – 0.69 = 0.31
This is the fraction of the volume of raft that is above the water.
Volume = 0.31 * π * 0.72075 = π * 0.2234325 m^3
BF = 1000 * 9.8 * π * 0.2234325= π * 2189.6385
This is approximately 6880 N. This is the weight of the people.
Number of people = π * 2189.6385 ÷ 656.6
This is approximately 10.5 people. So, 10 people is the answer.
For a log, density = 690 kg/m^3
For the raft to float, the buoyant force must be equal or greater than the total weight. Let’s use the following equation to determine the volume of a log in m^3.
Volume = π * r^2 * L, r = 0.31 m
Volume = π * 0.31^2 * 7.5 = π * 0.72075
This is approximately 2.264 m^3.
Let’s use the following equation to determine the mass of the raft.
Mass = Volume * density = π * 0.72075* 690 = π * 497.3175 kg
Weight = 9.8 * π * 497.3175 = π * 4873.7115 N
This is approximately 15,311N.
Buoyant force = Density of water * g * Volume of boat
Buoyant force = 1000 * 9.8 * π * 0.72075 = π * 7063.35
This is approximately 22,190 N. To determine the weight of the people, subtract the weight of the raft from the buoyant force.
Weight = π * 7063.35 – π * 4873.7115 = π * 2189.6385
This is approximately 6880 N.
Weight of one person = 67 * 9.8 = 656.6 N
Number of people = π * 2189.6385 ÷ 656.6
This is approximately 10.5 people. So, 10 people is the answer.
|
OR
To determine the fraction of the raft that is above water before the people get on it, subtract the specific gravity of the raft from the specific gravity of water.
1 – 0.69 = 0.31
This is the fraction of the volume of raft that is above the water.
Volume = 0.31 * π * 0.72075 = π * 0.2234325 m^3
BF = 1000 * 9.8 * π * 0.2234325= π * 2189.6385
This is approximately 6880 N. This is the weight of the people.
Number of people = π * 2189.6385 ÷ 656.6
This is approximately 10.5 people. So, 10 people is the answer.
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