To calculate the gravitational force exerted per unit of area by a column of mercury, we will use the formula for gravitational force:
F = mg
In this formula:
- F is the force in newtons (N),
- m is the mass in kilograms (kg),
- g is the acceleration due to gravity, which is approximately 9.81 m/s².
The pressure exerted by a column of fluid can be determined using the following relationship:
P = F/A
Where:
- P is the pressure in pascals (Pa),
- A is the area in square meters (m²).
For mercury, we know the density (ρ) is about 13,600 kg/m³. The height of the mercury column (h) also plays a crucial role. The mass of the mercury can be given by:
m = ρV = ρAh
Substituting this back into the force equation, we get:
F = ρAhg
Now substituting this into the pressure formula gives:
P = F/A = ρhg
Now we can plug in the values. For example, let’s say we have a column of mercury with a height of h = 1 meter:
P = 13,600 kg/m³ × 1 m × 9.81 m/s²
Calculating this:
P = 133,322.56 Pa
This means that a 1-meter column of mercury exerts a pressure of approximately 133,322.56 pascals on its base. This pressure is a representation of the gravitational force exerted per unit area by the column of mercury.