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?
A.Vr=300cm * 200cm * 20cm=1.2*10^6 cm^3 = Vol. of raft.
Dr = 6*10^5g / 1.2*10^6cm^3 = 0.5g/cm^3
= Density of raft with no load.
Vb = (Dr/Dw)*Vr.
Vb = (0.5/1)*1.2*10^6 = 6*10^5 cm^3 =
Vol. below surface = Vol of water displaced.
Ww = 6*10^5cm^3 * 1g/cm^3 = 6*10^5 g. =
600kg = Wt. of water displaced. = Buoyancy force
B. Drmax = Dw = 1g/cm^3 with full load.
Drmax = (6*10^5g+x)/1.2*10^6= 1.
6*10^5 + x = 1.2*10^6 .
X = 0.6*10^6 = 600kg = max load.
# People = 600kg / 65kg = 9, max.
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To determine the buoyant force, we need to use Archimedes' Principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
A) Determine the buoyant force:
Step 1: Calculate the volume of the wooden raft.
Volume = length x width x thickness
= 3 m x 2 m x 0.2 m
= 1.2 m³
Step 2: Convert the volume to liters (since 1 m³ = 1000 liters).
Volume = 1.2 m³ x 1000 liters/m³
= 1200 liters
Step 3: Convert liters to kilograms of water (1 liter = 1 kilogram).
Volume = 1200 kilograms
So, the buoyant force is 1200 kg.
B) Determine the number of 65-kg people the raft could support:
To calculate the maximum number of people the raft could support, we need to divide the weight the raft can support by the weight of a single person.
Step 1: Calculate the weight the raft can support.
Weight supported by raft = buoyant force - weight of the raft
= 1200 kg - 600 kg
= 600 kg
Step 2: Determine the number of people.
Number of people = Weight supported by raft / Weight of a single person
= 600 kg / 65 kg (rounded down to the nearest whole number)
= 9 people
Therefore, the raft can support a maximum of 9 people, assuming all the weight is evenly distributed on the raft.
To determine the buoyant force, you need to know the volume of water displaced by the raft. The buoyant force is equal to the weight of the water displaced, which can be calculated using the principle of Archimedes' buoyant force.
A) Determine the buoyant force:
To calculate the volume of water displaced by the raft, we need to find the volume of the raft itself. The volume of a rectangular solid can be calculated by multiplying its length, width, and height.
Volume of the raft = length x width x height
= 3 m x 2 m x 0.20 m (converting cm to meters)
= 1.2 m³
Since the raft is floating, the weight of the water displaced by the raft is equal to the buoyant force acting on it. The density of freshwater is approximately 1000 kg/m³.
Buoyant force = weight of the water displaced by the raft
= density of water x volume of water displaced x gravitational acceleration
= 1000 kg/m³ x 1.2 m³ x 9.8 m/s² (approximate value for gravity)
= 11,760 N
So, the buoyant force acting on the raft is 11,760 Newtons.
B) To calculate the number of people the raft can support, we need to consider the total weight that the raft can hold before sinking.
Total weight capacity = buoyant force - weight of the raft
= 11,760 N - 600 kg x 9.8 m/s² (approximate value for gravity)
= 11,760 N - 5,880 N
= 5,880 N
Now, to determine the number of people the raft can support, we need to divide the total weight capacity by the weight of a single person.
Number of people the raft can support = Total weight capacity / Weight of a single person
= 5,880 N / 65 kg x 9.8 m/s²
≈ 9 people (rounded down)
Therefore, the raft can support approximately 9 people weighing 65 kg each.