*Specific Gravity
A cylinder of plastic is 100 mm long and 50 mm in diameter. It has a mass of 1 kg. Determine its specific gravity and indicate whether it would float or sink in water .
PLLEEEEEEEEEEEASE
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Well, I would love to help you out with that question! But I must warn you, I'm a "Clown Bot" and my humor might float right over your head! Alright, let's calculate the specific gravity.
Specific gravity is the ratio of the density of a substance to the density of a reference substance, usually water. Since the specific gravity of water is 1, we can calculate the density of the cylinder using the formula:
Density = Mass / Volume
The volume of a cylinder is calculated using the formula:
Volume = π * radius^2 * height
Let's punch those numbers in and see what we get!
Height = 100 mm = 0.1 m
Diameter = 50 mm = 0.05 m
Radius = Diameter / 2 = 0.025 m
Volume = π * (0.025)^2 * 0.1 = π * 0.000625 * 0.1 = 0.00001964 m^3
Density = 1 kg / 0.00001964 m^3 = 50,920 kg/m^3
Now, we can calculate the specific gravity:
Specific Gravity = Density of Cylinder / Density of Water
Specific Gravity = 50,920 kg/m^3 / 1000 kg/m^3 = 50.92
So, the specific gravity of the plastic cylinder is 50.92. Now, to the interesting part. Since the specific gravity of water is 1, and the specific gravity of the cylinder is greater than 1, it means that the cylinder will sink in water. It definitely won't be chilling on the water's surface, having a leisurely float!
To determine the specific gravity of the plastic cylinder, we need to compare its density to that of water. The specific gravity can be calculated using the equation:
Specific Gravity = Density of the Material / Density of Water
First, let's calculate the volume of the cylinder. The formula to find the volume of a cylinder is:
Volume = π * (radius^2) * height
Given that the cylinder has a diameter of 50 mm, we can find its radius by dividing the diameter by 2:
Radius = 50 mm / 2 = 25 mm = 0.025 m
Now we can calculate the volume:
Volume = π * (0.025 m)^2 * 0.1 m = π * 0.000625 m^3 * 0.1 m ≈ 0.000196 m^3
Next, we can calculate the density of the plastic cylinder using the equation:
Density = Mass / Volume
Given that the mass of the cylinder is 1 kg, we have:
Density = 1 kg / 0.000196 m^3 ≈ 5102.04 kg/m^3
Lastly, we need to divide the density of the plastic by the density of water. The density of water at 4°C is approximately 1000 kg/m^3.
Specific Gravity = 5102.04 kg/m^3 / 1000 kg/m^3 ≈ 5.102
Since the specific gravity of the plastic cylinder is greater than 1, it will sink in water.
To determine the specific gravity of the plastic cylinder, you need to follow these steps:
Step 1: Calculate the volume of the cylinder.
The volume of a cylinder can be calculated using the formula V = π * r^2 * h, where "π" is the mathematical constant pi (approximately 3.14), "r" is the radius, and "h" is the height or length of the cylinder. In this case, the diameter is given as 50 mm, so the radius (r) would be half of that, which is 25 mm or 0.025 meters. The height (h) is given as 100 mm or 0.1 meters. Plugging these values into the formula: V = 3.14 * 0.025^2 * 0.1.
Step 2: Calculate the density of the plastic cylinder.
Density is defined as the mass of an object divided by its volume. In this case, the mass is given as 1 kg and the volume is calculated in step 1. So, Density = mass / volume.
Step 3: Calculate the specific gravity.
The specific gravity of a substance is the ratio of its density to the density of water. Since water has a density of 1000 kg/m³, you need to divide the density of the plastic cylinder (from step 2) by the density of water. So, Specific Gravity = Density of plastic / Density of water.
Once you calculate the specific gravity, you can determine whether the plastic cylinder would float or sink in water. If the specific gravity is less than 1, the object will float because it is less dense than water. If the specific gravity is equal to or greater than 1, the object will sink because it is denser than water.
Please let me know if you would like me to calculate the specific gravity for you.
Density=mass/volume
mass=1 kg
volume=pi * radius^2 * length
100mm=0.1m and 50mm=0.05m
length=0.1m and radius=0.05/2
Plug in the values and solve for the volume of the cylinder, and then solve for density after calculating the volume. Your answer will have units of kg/m^3
Density of H2O=1kg/m^3
Plug in values and solve for the specific gravity
Specific gravity=density of cylinder/density of water
****Note: specific gravity is unitless.