A 7.2 cm tall cylinder floats in water with its axis perpendicular to the surface. The length of the cylinder above water is 1.4 cm. What is the cylinder's mass density?
wouldn't it be (7.2-1.4)/7.2 *density water?
To find the mass density of the cylinder, we need to identify the volume of the cylinder and its mass.
Step 1: Calculate the volume of the cylindrical shape above the water:
The height of the above-water portion of the cylinder is 1.4 cm.
Since the axis of the cylinder is perpendicular to the water surface, the above-water portion is in the shape of a cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
The radius of the above-water portion can be calculated by subtracting the radius of the entire cylinder (7.2 cm) from the radius of the submerged portion (which is the radius of the entire cylinder).
The radius of the submerged portion is 7.2 cm - 1.4 cm = 5.8 cm.
Therefore, the volume of the above-water portion is V = π(5.8 cm)^2(1.4 cm).
Step 2: Calculate the mass of the cylinder:
The mass of an object can be calculated as the product of its volume and mass density: m = ρV, where m is the mass, ρ is the mass density, and V is the volume.
We are given the length of the cylinder above water (1.4 cm), but we need to find the mass density.
Therefore, we cannot directly calculate the mass using the given information. We need additional information, such as the mass or the mass density.
Conclusion:
Since we do not have the necessary information to directly calculate the mass or the mass density of the cylinder, we cannot determine the cylinder's mass density based on the given information.
To find the cylinder's mass density, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Here's how to get the answer:
1. Determine the volume of the submerged part of the cylinder:
- The submerged length of the cylinder is given as 1.4 cm.
- The height of the cylinder is given as 7.2 cm, so the part above water is 7.2 - 1.4 = 5.8 cm.
- Since the shape of the cylinder is symmetric, the submerged part also has a height of 5.8 cm.
- The cross-sectional area of the cylinder can be found by multiplying the radius squared by pi (A = πr^2).
2. Calculate the weight of the water displaced by the submerged part of the cylinder:
- The volume of water displaced is equal to the volume of the submerged part of the cylinder.
- Multiply the cross-sectional area (from step 1) by the height of the submerged part (5.8 cm) to get the volume.
- Multiply the volume by the density of water, which is approximately 1 g/cm^3, to find the weight in grams.
3. Convert the weight from grams to kilograms:
- Divide the weight in grams by 1000 to get the weight in kilograms.
4. Divide the weight in kilograms by the volume of the entire cylinder to calculate the mass density:
- The volume of the entire cylinder can be found by multiplying the cross-sectional area (from step 1) by the total height of the cylinder (7.2 cm).
- Divide the weight in kilograms by the volume in cubic meters (divide by 10000 to convert cm^3 to m^3).
This will give you the mass density of the cylinder in kg/m^3.