A raft is made of wood with a density of 404 kg/m^3. It is 42 cm thick and its square area is 3.0x3.0 m^2. It is floating in seawater (density = 1025 kg/m^3). How many people of 68 kilogram can the raft hold before they start getting their feet wet?
Are they hanging the feet over the side? :_)
well, the bouyancy has to equal the weight.
weightwood+weightpeople=.42*3x3*1025*9.8N
No, I would guess they are just standing in the raft. Where does the 68 kg come into this?
We also know that when the raft is empty it is 61% above the water.
To determine how many people the raft can hold before they start getting their feet wet, we need to compare the weight of the raft with the weight it displaces in the water.
First, let's calculate the weight of the raft:
The volume of the raft can be calculated by multiplying the area of the square base by its thickness:
Volume of the raft = Area x Thickness = 3.0 m^2 x 0.42 m (converted from 42 cm to meters) = 1.26 m^3
Using the density of wood (404 kg/m^3), we can calculate the weight of the raft:
Weight of the raft = Density x Volume = 404 kg/m^3 x 1.26 m^3 = 509.04 kg
Now, let's calculate the weight of the water displaced by the raft:
The volume of water displaced by the raft is equal to its volume:
Volume of displaced water = Volume of the raft = 1.26 m^3
Using the density of seawater (1025 kg/m^3), we can calculate the weight of the displaced water:
Weight of displaced water = Density x Volume = 1025 kg/m^3 x 1.26 m^3 = 1288.5 kg
To find out how many people the raft can hold, we need to subtract the weight of the raft from the weight of the displaced water, and then divide by the weight of each person:
Total weight the raft can hold = (Weight of displaced water - Weight of the raft) / Weight per person
Weight per person = 68 kg
Total weight the raft can hold = (1288.5 kg - 509.04 kg) / 68 kg
Total weight the raft can hold = 779.46 kg / 68 kg ≈ 11.45
Therefore, the raft can hold approximately 11 people of 68 kilograms each before they start getting their feet wet.