What is the pressure at the bottom of a tube of mercury that is 0.2 m deep?
An elephant with a mass of 1000 kg stands on a circus platform that weighs 50 kg. The area of the bottom of the platform is 1.25 m². How much pressure is exerted on the floor beneath the platform?
Two barometers are identical except that one is filled with water while the other is filled with benzene. In which barometer will the liquid rise higher, and by how much?
If you increase the pressure on the air inside a cylinder to three times its original value, the volume of the air inside the cylinder will be ____________________.
To calculate the pressure at the bottom of a tube of mercury, you need to use the formula for pressure, which is given as:
Pressure = Density × Gravitational Acceleration × Height
First, you need to identify the values given in the problem. The density of mercury is approximately 13,600 kg/m³, and the standard gravitational acceleration is 9.8 m/s².
Plugging those values into the formula, you get:
Pressure = (13,600 kg/m³) × (9.8 m/s²) × (0.2 m)
Simplifying the equation:
Pressure = 26,720 Pa
Therefore, the pressure at the bottom of the tube of mercury 0.2 m deep is 26,720 Pa.
To calculate the pressure exerted by the elephant on the floor beneath the platform, you need to use the formula for pressure, which is given as:
Pressure = Force/Area
First, you need to calculate the force exerted by the elephant. The formula for force is given as:
Force = Mass × Acceleration
The mass of the elephant is given as 1000 kg, and the acceleration due to gravity is approximately 9.8 m/s².
Plugging those values into the formula, you get:
Force = (1000 kg) × (9.8 m/s²)
Simplifying the equation:
Force = 9800 N
Next, you need to calculate the total weight of the elephant and the platform:
Total Weight = Weight of Elephant + Weight of Platform
The weight of the elephant is calculated using the formula:
Weight = Mass × Gravitational Acceleration
Plugging in the given values:
Weight of Elephant = (1000 kg) × (9.8 m/s²)
Simplifying the equation:
Weight of Elephant = 9800 N
The weight of the platform is given in the problem as 50 kg. Therefore:
Weight of Platform = (50 kg) × (9.8 m/s²)
Simplifying the equation:
Weight of Platform = 490 N
Now, you can calculate the total weight:
Total Weight = 9800 N + 490 N
Simplifying the equation:
Total Weight = 10290 N
Finally, you can calculate the pressure:
Pressure = (10290 N) / (1.25 m²)
Simplifying the equation:
Pressure = 8232 Pa
Therefore, the pressure exerted on the floor beneath the platform by the elephant is 8232 Pa.
For the two barometers filled with water and benzene, the liquid will rise higher in the barometer filled with benzene compared to the one filled with water. This is because benzene is denser than water. The difference in the height to which the liquid rises will depend on the densities of water and benzene.
To calculate the increase in pressure on the air inside a cylinder when the pressure is increased to three times its original value, you can use Boyle's Law which states that the volume of a gas is inversely proportional to its pressure.
Let's say the initial pressure is P and the initial volume is V. According to Boyle's Law:
P₁ × V₁ = P₂ × V₂
If the initial pressure is P and it is increased to three times its original value (3P), the new pressure is 3P.
We can assume that the initial volume V remains the same.
Plugging these values into the equation:
P × V = (3P) × V₂
Simplifying the equation:
V₂ = V/3
Therefore, the volume of the air inside the cylinder will be one-third of its original volume when the pressure on the air is increased to three times its original value.
To calculate the pressure at the bottom of a tube of mercury:
1. Identify the density of mercury, which is approximately 13,600 kg/m^3.
2. Multiply the density of mercury by the depth of the tube (0.2 m) and the acceleration due to gravity (9.8 m/s^2):
Pressure = density × depth × gravity
Pressure = 13,600 kg/m^3 × 0.2 m × 9.8 m/s^2
To calculate the pressure exerted by an elephant on a circus platform:
1. Calculate the total weight of the elephant and the platform:
Weight = mass × gravity
Weight = (1000 kg + 50 kg) × 9.8 m/s^2
2. Divide the total weight by the area of the bottom of the platform:
Pressure = Weight / Area
Pressure = (1000 kg + 50 kg) × 9.8 m/s^2 / 1.25 m²
Regarding the two barometers filled with water and benzene, the liquid will rise higher in the barometer with water because it has a higher density than benzene. The actual difference in the liquid levels will depend on the specific densities of water and benzene.
If you increase the pressure on the air inside a cylinder to three times its original value, the volume of the air inside the cylinder will decrease. This relationship is described by Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure when the temperature remains constant.