A cylindrical object 0.5m in diameter and 2m long weights has a mass of 200kg. The object is floating end-down in water. How many cm of the object are above the waterline?
A =cross section area = pi (.5)^2
1000 Kg/m^3 * A * (2-L) = mass of water displaced = 200
solve for L, multiply by 100 to get cm instead of meters
To find out how many centimeters of the object are above the waterline, we first need to calculate the volume of the object.
The volume of a cylinder can be calculated using the formula:
V = π * r^2 * h
Where:
V is the volume
π is a mathematical constant, approximately equal to 3.14159
r is the radius of the cylinder (half the diameter)
h is the height or length of the cylinder
Given:
Diameter (d) = 0.5m
Radius (r) = d/2 = 0.25m
Height (h) = 2m
Now, let's calculate the volume of the cylindrical object:
V = 3.14159 * (0.25)^2 * 2
V ≈ 0.3927 cubic meters
Since the object is floating end-down in water, the volume of water displaced is equal to the volume of the object. This principle is known as Archimedes' principle.
Now, to find out how many centimeters of the object are above the waterline, we need to calculate the height of the part submerged in water.
Given:
Density of water = 1000 kg/m^3 (approximately)
Mass of the object = 200 kg (given)
We can calculate the submerged height using the formula:
Submerged height = V_object / (π * r^2)
Now let's substitute the values and calculate the submerged height:
Submerged height = 0.3927 / (3.14159 * (0.25)^2)
Submerged height ≈ 1.254 meters
Finally, to find the height above the waterline in centimeters, we can subtract the submerged height from the total height of the cylinder.
Height above waterline = Total height - Submerged height
Height above waterline = 2 - 1.254
Height above waterline ≈ 0.746 meters
Converting meters to centimeters:
Height above waterline = 0.746 * 100
Height above waterline ≈ 74.6 centimeters
Therefore, approximately 74.6 centimeters of the object are above the waterline.