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.
I tried (1025-917)/27=4 and it's not correct. I'm probably just missing something silly, but every other way I've tried it doesn't make any sense
a) To find the answer, we can use Archimedes' Principle, which states that the buoyant force acting on an object equals the weight of the fluid it displaces. In this case, the buoyant force acting on the ice block equals the weight of the water it displaces.
The weight of the water displaced is given by the formula:
Weight = Volume x Density x Acceleration due to gravity
The volume of the water displaced is equal to the volume of the ice block that is submerged. Given that the ice block is a rectangular prism with dimensions 10 m x 10 m x 1.1 m, the volume of the submerged portion is 10 m x 10 m x h, where h is the height submerged.
Since the density of ice is 917 kg/m3, the density of the water displaced by the submerged portion is also 917 kg/m3. Therefore, the weight of the water displaced is given by:
Weight = (10 m x 10 m x h) x 917 kg/m3 x 9.8 m/s2
Now, we know that the buoyant force acting on the ice block is equal to its weight when it is floating. Therefore, we can set the weight of the water displaced equal to the weight of the ice block:
(10 m x 10 m x h) x 917 kg/m3 x 9.8 m/s2 = (10 m x 10 m x 1.1 m) x 917 kg/m3 x 9.8 m/s2
We can cancel out the density and acceleration due to gravity on both sides, giving us:
h = 1.1 m
So, the top of the ice block floats 1.1 m above the water level.
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 maximum weight the ice block can support before it sinks.
The weight of the ice block is given by:
Weight of ice block = Volume of ice block x Density of ice x Acceleration due to gravity
The volume of the ice block is given by:
Volume of ice block = Length x Width x Height = 10 m x 10 m x 1.1 m
Thus, the weight of the ice block is:
Weight of ice block = (10 m x 10 m x 1.1 m) x 917 kg/m3 x 9.8 m/s2
To determine how many penguins the ice block can support, we divide the weight of the ice block by the weight of each penguin.
Number of penguins = Weight of ice block / Weight of each penguin
So, the answer is:
Number of penguins = [(10 m x 10 m x 1.1 m) x 917 kg/m3 x 9.8 m/s2] / (27 kg)
Approximately 415 penguins can stand on the ice block before their feet get wet. The result is rounded to the nearest whole number.
a) To determine how high the top of the ice block floats above the water level, we can use Archimedes' Principle. According to Archimedes' Principle, an object displaces its weight in fluid.
To calculate the height, we need to compare the densities of the ice and the sea water. The buoyant force acting on the ice block is equal to the weight of the water displaced by the ice.
Density of ice = 917 kg/m^3
Density of sea water = 1025 kg/m^3
So, the density difference between the ice and the seawater is:
Density difference = Density of sea water - Density of ice
Density difference = 1025 kg/m^3 - 917 kg/m^3
Density difference = 108 kg/m^3
Now, we can calculate the buoyant force exerted on the ice block using the formula:
Buoyant force = Density difference x Volume of the ice block x gravitational acceleration
Volume of the ice block = Length x Width x Height
Volume of the ice block = 10 m x 10 m x 1.1 m
Volume of the ice block = 110 m^3
Gravitational acceleration = 9.8 m/s^2
Buoyant force = 108 kg/m^3 x 110 m^3 x 9.8 m/s^2
Buoyant force = 117312 N
The weight of the ice block can be calculated using the formula:
Weight of the ice block = Density of ice x Volume of the ice block x gravitational acceleration
Weight of the ice block = 917 kg/m^3 x 110 m^3 x 9.8 m/s^2
Weight of the ice block = 1005632 N
Since the buoyant force is equal to the weight of the ice block, the top of the ice block will float at the same level as the water. Therefore, the height of the top of the ice block above the water level is 0 meters.
b) To determine the number of penguins that can stand on the ice block before their feet get wet, we need to consider the weight of both the penguins and the ice block. The ice block will sink if the combined weight of the penguins exceeds the buoyant force acting on the ice block.
We already calculated the weight of the ice block, which is 1005632 N.
Let's assume the number of penguins is represented by "n".
The weight of n penguins is equal to the mass of one penguin multiplied by the number of penguins:
Weight of n penguins = Mass of one penguin x n x gravitational acceleration
Given that the mass of one penguin is 27 kg, we can now set up the equation:
Weight of n penguins = 27 kg x n x 9.8 m/s^2
For the penguins' feet to stay dry, the buoyant force exerted on the ice block should be greater than or equal to the combined weight of the penguins.
Buoyant force >= Weight of n penguins
117312 N >= 27 kg x n x 9.8 m/s^2
Simplifying the equation:
117312 N >= 264.6 N x n
Dividing both sides by 264.6 N:
442.947 >= n
Since the number of penguins must be a whole number, we can conclude that the maximum number of penguins that can stand on the ice block without their feet getting wet is 442 penguins.