when inflated, a rubber lifeboat takes the form of rectangular box of dimensions 2mx1.5x40cm. with out any load, it floats. how many 60kg people can it carry before water flows into it? assume that the density of seawater is 1025g/cubic meter.
Is the 1.5 dimension meters?
Are those inside (passenger area) or outside dimensions?
To determine how many people the rubber lifeboat can carry before water flows into it, we need to compare the weight of the people to the buoyancy provided by the lifeboat.
First, let's convert the dimensions of the lifeboat to meters for consistency:
Length (L) = 2m
Width (W) = 1.5m
Height (H) = 0.4m
The volume of the lifeboat can be calculated as:
Volume (V) = L × W × H
Substituting the values:
V = 2m × 1.5m × 0.4m
V = 1.2 cubic meters
The weight of the lifeboat is given to be 0 kg since it floats without any load.
Next, we need to calculate the weight of the water displaced by the lifeboat. The density of seawater is given to be 1025g/cubic meter.
The weight of the water displaced (W_displaced) can be calculated as:
W_displaced = density × V
Substituting the values:
W_displaced = 1025g/cubic meter × 1.2 cubic meters
W_displaced = 1230 kg
Since the lifeboat can carry its own weight (0 kg), the remaining buoyancy available is:
Buoyancy = W_displaced - Weight of lifeboat
Buoyancy = 1230 kg - 0 kg
Buoyancy = 1230 kg
To determine how many 60 kg people the lifeboat can carry, we divide the total buoyancy by the weight of each person:
Number of people = Buoyancy / Weight of each person
Number of people = 1230 kg / 60 kg
Number of people ≈ 20.5
Therefore, the rubber lifeboat can carry approximately 20 people (ignoring fractional people) before water flows into it.
To determine the number of 60kg people the rubber lifeboat can carry before water flows into it, we need to calculate the total weight supported by the lifeboat and compare it to its buoyancy.
First, let's convert the dimensions of the lifeboat into meters. The dimensions are:
Length (L) = 2m
Width (W) = 1.5m
Height (H) = 0.4m
The weight of the lifeboat itself can be calculated using its volume and the density of rubber—the density of rubber is about 1100 kg/cubic meter. Since the boat is in the shape of a rectangular box, its volume can be calculated as:
Volume of the lifeboat = Length x Width x Height
Volume of the lifeboat = 2m x 1.5m x 0.4m
Volume of the lifeboat = 1.2 cubic meters
The weight of the lifeboat is then calculated as:
Weight of the lifeboat = Volume of the lifeboat x Density of rubber
Weight of the lifeboat = 1.2 cubic meters x 1100 kg/cubic meter
Next, we need to calculate the buoyancy of the lifeboat. The buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is seawater.
The buoyant force can be calculated as:
Buoyant force = Weight of the fluid displaced
Buoyant force = Density of seawater x Volume of the lifeboat
Now, let's calculate the total weight the lifeboat can support before water flows into it:
Total weight supported = Buoyant force - Weight of the lifeboat
To determine the number of people the lifeboat can carry, divide the total weight supported by the weight of each person:
Number of people = Total weight supported / Weight of each person
Let's plug in the values:
Density of seawater = 1025 kg/cubic meter
Density of rubber = 1100 kg/cubic meter
Weight of each person = 60 kg
By performing the calculations, you should be able to determine the number of 60kg people the lifeboat can carry before water flows into it.