1. A cylinder tank is 30m deep,calculate the pressure extended at the bottom of the tank,when it is four-fifth filled with water (g=10mg-2,density of water =1000kgm-2) 2.a sample of air weighing 1.32*10^2N is confined in a room measuring 9.5m*2.0m.calculate the density of the sample
1. Pressure at the bottom of the tank = (density of water x gravitational acceleration x depth of tank) = (1000 kg/m^3 x 10 m/s^2 x 30 m) = 3 x 10^5 Pa
2. Density of the sample = (weight of the sample / volume of the room) = (1.32 x 10^2 N / (9.5 m x 2.0 m)) = 7.03 kg/m^3
1. Well, let's dive into this question! The pressure at the bottom of the cylinder tank can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height or depth.
Given that the cylinder tank is 30m deep and four-fifth filled with water, we can calculate the height of the water using 4/5 * 30m = 24m.
Now, let's plug in the values into our pressure formula:
P = (1000kg/m³) * (10m/s²) * (24m)
P = 240,000 Pascal.
So, the pressure at the bottom of the tank (when it's four-fifth filled with water) is approximately 240,000 Pascal. That's quite a heavy splash!
2. Ah, here comes the density dilemma! To figure out the density of the air sample, we'll need to divide its weight (1.32 * 10² N) by its volume.
The volume of the room is given as 9.5m * 2.0m = 19m².
Now, let's calculate the density by dividing the weight by volume:
Density = Weight / Volume
Density = (1.32 * 10² N) / 19m²
Well, I seem to have hit a bit of a snag! Unfortunately, the units don't match up. You can't divide Newtons by square meters. It's like trying to divide apples by cats – it just doesn't make sense. Could you double-check the units or provide additional information? I'd be happy to try and help again!
1. To calculate the pressure at the bottom of the tank, we can use the formula:
Pressure = Density × g × Height
Given:
- Cylinder tank depth = 30 m
- Water density = 1000 kg/m³
- Acceleration due to gravity (g) = 10 m/s²
The tank is four-fifths filled with water, so the depth of the water is 30 m x 4/5 = 24 m.
Using the formula, we can plug in the values:
Pressure = 1000 kg/m³ × 10 m/s² × 24 m
Calculating the pressure:
Pressure = 240,000 Pascal (Pa)
Therefore, the pressure at the bottom of the tank, when it is four-fifths filled with water, is 240,000 Pa.
2. To calculate the density of the air sample, we can use the formula:
Density = Mass / Volume
Given:
- Weight of the air sample = 1.32 × 10² N (Newton)
- Room dimensions = 9.5 m × 2.0 m
First, let's convert the weight from Newton to kg using the relation 1 N = 1 kg · m/s²:
Weight = 1.32 × 10² N = 1.32 × 10² kg · m/s²
The weight of the air sample is equal to the force acting on it due to gravity, which is equal to its mass multiplied by the acceleration due to gravity (F = mg). So, we can write:
Mass × g = Weight
Solving for mass (m):
Mass = Weight / g
Now, let's calculate the mass by plugging in the values:
Mass = 1.32 × 10² kg · m/s² / 10 m/s²
Mass = 13.2 kg
Next, we can calculate the volume of the room:
Volume = Length × Width × Height
Volume = 9.5 m × 2.0 m × 1 m (assuming the height of the room is 1m)
Volume = 19 m³
Finally, we can calculate the density using the formula:
Density = Mass / Volume
Density = 13.2 kg / 19 m³
Calculating the density:
Density ≈ 0.694 kg/m³
Therefore, the density of the air sample is approximately 0.694 kg/m³.
To calculate the pressure at the bottom of the cylinder tank, we can use the formula:
Pressure = Density * Gravity * Height
First, let's calculate the height of the water in the tank when it is four-fifths filled.
If the total depth of the tank is 30m, and it is four-fifths filled, then the height of the water will be:
Height of water = Total depth * (4/5)
Height of water = 30m * (4/5)
Height of water = 24m
Now, we can calculate the pressure at the bottom of the tank.
Given:
Density of water = 1000 kg/m^3 (density is given in kg/m^3)
Gravity = 10 m/s^2 (acceleration due to gravity)
Pressure = Density * Gravity * Height
Pressure = 1000 kg/m^3 * 10 m/s^2 * 24m
Pressure = 240,000 Pa
Therefore, the pressure at the bottom of the tank, when it is four-fifths filled with water, is 240,000 Pa (Pascals).
Now, let's move on to the second question.
To calculate the density of the air sample, we can use the formula:
Density = Mass / Volume
Given:
Weight of the air sample = 1.32 * 10^2 N (weight is given in Newtons)
Area of the room = 9.5 m * 2.0 m = 19 m^2 (area is given in square meters)
First, let's calculate the mass of the air sample using the weight:
Weight = Mass * Gravity
Mass = Weight / Gravity
Mass = (1.32 * 10^2 N) / (10 m/s^2)
Mass = 13.2 kg
Now, we can calculate the volume of the air sample using the area of the room:
Volume = Area * Height (assuming the height is unknown)
Height = Volume / Area
Since the height is unknown, we cannot calculate the density directly.
Please provide additional details such as the height or any other relevant information in order to calculate the density of the air sample.