A rectangular block of ice 10 m on each side and 1.1 m thick floats in sea water. The density of the sea water is 1025 kg/m3. The density of ice is 917 kg/m3.
a) How high does the top of the ice block float above the water level?
m *
.116 OK
HELP: Use Archimedes' Priciple.
b) How many penguins of mass 27 kg each can stand on the ice block before they get their feet wet?
4 NO
HELP: Their feet will get wet if the ice block sinks below the water surface.
Just need b
total volume of ice = 100*1.1 = 110m^3
mass of ice = 917*110 = 100870 kg
that is the mass of water displaced (Archimedes)
so
volume of water displaced = 100870/1025
=98.41m^3
so
100m^2 * x = 98.41 where x is the draft
x = .984 m
so height out of water = 1.1-.984 = .116m
added mass of penguins = 27 n
mass of water displaced by penquin mass = 1025*100*.116
so
27 n = 1025*100*.116
n = 440
To find out how many penguins of mass 27 kg each can stand on the ice block before their feet get wet, we need to determine the maximum mass the ice block can support before sinking below the water surface.
The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Based on Archimedes' Principle, the buoyant force can be calculated as:
Buoyant force = Weight of the fluid displaced by the object = Density of the fluid * Volume of the fluid displaced * g
In this case, the fluid is sea water, which has a density of 1025 kg/m³. The volume of the fluid displaced by the ice block is equal to the volume of the submerged portion of the ice block.
Given that the dimensions of the ice block are 10 m by 10 m by 1.1 m, the volume of the ice block is:
Volume of the ice block = Length * Width * Thickness = 10 m * 10 m * 1.1 m
Since the ice block is fully submerged, the volume of the submerged portion is equal to the volume of the ice block. Therefore, the volume of the fluid displaced by the ice block is also equal to the volume of the ice block.
Now, to calculate the buoyant force, we need to multiply the density of the fluid (sea water) by the volume of the fluid displaced and the acceleration due to gravity (9.8 m/s²):
Buoyant force = 1025 kg/m³ * Volume of the ice block * 9.8 m/s²
Using the volume of the ice block, we can calculate the buoyant force.
Next, we need to determine the maximum mass that the ice block can support without sinking. This is equal to the buoyant force acting on the ice block.
Maximum mass supported = Buoyant force
Finally, we divide the maximum mass supported by the mass of each penguin (27 kg) to find out how many penguins can stand on the ice block before their feet get wet.
Number of penguins = Maximum mass supported / Mass of each penguin
Now, using the given values and the equations and steps mentioned above, you can calculate the answer to part b).
To determine how many penguins of mass 27 kg each can stand on the ice block before their feet get wet, we need to consider the buoyancy force exerted by the water on the ice block.
The buoyancy force is equal to the weight of the displaced water. According to Archimedes' Principle, the buoyancy force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Step 1: Calculate the weight of the ice block:
The volume of the ice block is given by:
Volume = length × width × height = 10 m × 10 m × 1.1 m = 110 m³
The mass of the ice block is given by:
Mass = Density × Volume = 917 kg/m³ × 110 m³ = 100,870 kg
The weight of the ice block is given by:
Weight = Mass × Gravity = 100,870 kg × 9.8 m/s² = 988,946 N
Step 2: Calculate the weight of the displaced water:
The volume of water displaced is equal to the volume of the submerged portion of the ice block. Since the entire ice block is floating, the height submerged is equal to the height of the ice block.
Volume of water displaced = length × width × height submerged = 10 m × 10 m × 1.1 m = 110 m³
The mass of the displaced water is given by:
Mass of displaced water = Density of seawater × Volume of water displaced = 1025 kg/m³ × 110 m³ = 112,750 kg
The weight of the displaced water is given by:
Weight of displaced water = Mass of displaced water × Gravity = 112,750 kg × 9.8 m/s² = 1,105,150 N
Step 3: Calculate the buoyancy force:
Buoyancy force = Weight of displaced water = 1,105,150 N
Step 4: Calculate the maximum additional weight the ice block can support:
The maximum additional weight that the ice block can support is equal to the buoyancy force.
Maximum additional weight = Buoyancy force = 1,105,150 N
Step 5: Calculate the number of penguins that can stand on the ice block:
Since each penguin has a mass of 27 kg, the number of penguins that can stand on the ice block without sinking it is given by:
Number of penguins = Maximum additional weight ÷ Mass of each penguin
= 1,105,150 N ÷ 27 kg
≈ 40,928 penguins
Therefore, approximately 40,928 penguins of mass 27 kg each can stand on the ice block before their feet get wet.