1. What is the pressure on the bottom of an aquarium 0.30 m deep filled with water?
2. The plug in a bathtub is 10 cm^3in area and is 0.8 m below the surface of the water. What is the force of the water on the plug?
3. If a column of oil 0.89 m high in balanced by a column of mercury 0.06 m high, what is density of oil?
2900 N/m^2
2.94 n/m^2
1. To calculate the pressure on the bottom of the aquarium, we can use the formula: pressure = density x gravity x height.
Given:
density of water = 1000 kg/m³ (assuming the density of water)
gravity = 9.8 m/s² (acceleration due to gravity)
height = 0.30 m
Substituting the values into the formula:
pressure = 1000 kg/m³ x 9.8 m/s² x 0.30 m
Calculating the pressure:
pressure = 294 Pa (Pascal)
Therefore, the pressure on the bottom of the aquarium is 294 Pascal.
2. To determine the force of the water on the plug, we can use the equation: force = pressure x area.
Given:
pressure = density x gravity x height (using the same values as in question 1)
area = 10 cm² = 0.001 m² (since 1 cm² = 0.0001 m²)
Substituting the values into the equation:
force = 294 Pa x 0.001 m²
Calculating the force:
force = 0.294 N (Newton)
Therefore, the force of the water on the plug is 0.294 Newton.
3. To find the density of oil, we can use the equation: density = pressure / (gravity x height).
Given:
pressure of oil column = pressure of mercury column
height of oil = 0.89 m
height of mercury = 0.06 m
density of mercury = 13593 kg/m³ (known value)
Substituting the values into the equation:
density of oil = density of mercury x (height of mercury / height of oil)
Calculating the density of oil:
density of oil = 13593 kg/m³ x (0.06 m / 0.89 m)
density of oil ≈ 919.88 kg/m³
Therefore, the density of oil is approximately 919.88 kg/m³.
1. To calculate the pressure on the bottom of an aquarium filled with water, we can use the formula for pressure: P = ρgh, where P is the pressure, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity, and h is the depth of the fluid.
- Step 1: Identify the known values:
- Depth (h) = 0.30 m.
- Density (ρ) of water = 1000 kg/m³ (approximately).
- Step 2: Use the formula P = ρgh and plug in the values:
P = (1000 kg/m³) * (9.8 m/s²) * (0.30 m).
- Step 3: Solve the equation:
P = 2940 Pa (Pascal).
Therefore, the pressure on the bottom of the aquarium 0.30 m deep filled with water is 2940 Pascal.
2. To calculate the force of water on the plug in a bathtub, we can use the formula for pressure again: P = ρgh. Then, we can find the force by multiplying the pressure by the area of the plug.
- Step 1: Identify the known values:
- Depth (h) = 0.8 m.
- Density (ρ) of water = 1000 kg/m³ (approximately).
- Area (A) of the plug = 10 cm² (convert to meters by dividing by 10,000: 0.001 m²).
- Step 2: Use the formula P = ρgh and plug in the values to find the pressure:
P = (1000 kg/m³) * (9.8 m/s²) * (0.8 m).
- Step 3: Calculate the force by multiplying the pressure by the area:
Force = P * A = (Pressure) * (Area).
Therefore, the force of the water on the plug is:
Force = (1000 kg/m³ * 9.8 m/s² * 0.8 m) * (0.001 m²) = 7.84 Newtons.
3. To determine the density of oil in a balanced column setup, we can use the principle of hydrostatic equilibrium. The pressure exerted by each fluid column is directly proportional to its height and density.
- Step 1: Identify the known values:
- Height of the oil column (h₁) = 0.89 m.
- Height of the mercury column (h₂) = 0.06 m.
- Density of mercury (ρₘ) = 13,600 kg/m³ (approximately).
- Step 2: Set up the equation that represents the balance of the two fluid columns:
Pressure exerted by oil = Pressure exerted by mercury.
(ρ₁ * g * h₁) = (ρ₂ * g * h₂).
- Step 3: Rearrange the equation to solve for the unknown density of oil (ρ₁):
ρ₁ = (ρ₂ * g * h₂) / (g * h₁).
- Step 4: Calculate the density of oil by substituting the known values:
ρ₁ = (13,600 kg/m³ * 9.8 m/s² * 0.06 m) / (9.8 m/s² * 0.89 m).
Therefore, the density of oil is approximately 979.55 kg/m³.