A wooden raft 3 m long x 2 m wide x 20 cm thick floats on a freshwater lake. A) Determine the buoyant force? B) If the raft itself has a mass of 600 kg, how many 65-kg people could it support?
To determine the buoyant force on the wooden raft, we need to first calculate the volume of the wooden raft. The volume can be calculated using the formula:
Volume = length x width x thickness
Substituting the given values, we have:
Volume = 3 m x 2 m x 0.20 m
Next, we need to determine the density of the freshwater. The density of freshwater is approximately 1000 kg/m³.
Now we can calculate the buoyant force using Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Buoyant Force = Volume x Density of Fluid x Gravitational Acceleration
Buoyant Force = (3 m x 2 m x 0.20 m) x 1000 kg/m³ x 9.8 m/s²
Now let's calculate the buoyant force:
Buoyant Force = 12 m³ x 1000 kg/m³ x 9.8 m/s²
Buoyant Force = 117,600 N
So, the buoyant force acting on the wooden raft is 117,600 N.
Now, to determine how many 65-kg people the raft could support, we need to compare the total weight of the people to the buoyant force.
The total weight of the people that the raft can support is equal to the maximum weight the raft can support without sinking, which is equal to the buoyant force.
So, to find the number of people the raft can support, we divide the buoyant force by the weight of one person.
Number of People = Buoyant Force / Weight of One Person
Number of People = 117,600 N / 65 kg
Now let's calculate the number of people the raft can support:
Number of People = 1809.23
Therefore, the wooden raft can support approximately 1809 people.
A) To determine the buoyant force on the wooden raft, we can use the formula:
Buoyant force = Volume of the displaced water x Density of water x Acceleration due to gravity
1. First, we need to calculate the volume of the displaced water. Since the raft floats on the water, it displaces a volume equal to its own volume.
Volume of the raft = length x width x height
= 3 m x 2 m x 0.20 m (convert thickness from cm to m)
= 1.2 m³
2. The density of freshwater is approximately 1000 kg/m³.
3. The acceleration due to gravity is approximately 9.8 m/s².
Now, we can calculate the buoyant force:
Buoyant force = 1.2 m³ x 1000 kg/m³ x 9.8 m/s²
= 11,760 N
Therefore, the buoyant force on the raft is 11,760 Newtons.
B) To determine the number of 65-kg people the raft could support, we need to compare the weight of the raft (including people) with the buoyant force.
1. The weight of the raft is equal to the mass of the raft multiplied by the acceleration due to gravity:
Weight of the raft = Mass of the raft x Acceleration due to gravity
= 600 kg x 9.8 m/s²
= 5880 N
2. To find out how many people it could support, we divide the weight of the raft by the weight of one person:
Number of people = Weight of the raft / Weight of one person
= 5880 N / 65 kg x 9.8 m/s²
≈ 9
Therefore, the raft could support approximately 9 people.