Average density of continental crust is 2.5 gm/cc. calculate pressure at the base of 35 km of continental crust?
The Correct Answer and Explanation is :
To calculate the pressure at the base of 35 km of continental crust, we can use the formula for pressure, which is:
[
P = \rho \cdot g \cdot h
]
Where:
- ( P ) is the pressure,
- ( \rho ) is the density of the crust,
- ( g ) is the acceleration due to gravity, and
- ( h ) is the height (depth) of the crust.
Given Data:
- Density of continental crust ( \rho = 2.5 \, \text{g/cm}^3 = 2500 \, \text{kg/m}^3 ),
- Acceleration due to gravity ( g = 9.81 \, \text{m/s}^2 ),
- Height ( h = 35 \, \text{km} = 35,000 \, \text{m} ).
Calculation:
Now, we can substitute the values into the formula:
[
P = 2500 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 35,000 \, \text{m}
]
Let’s calculate the pressure:
[
P = 2500 \cdot 9.81 \cdot 35,000
]
[
P = 868,875,000 \, \text{Pa} = 868.9 \, \text{MPa}
]
So, the pressure at the base of 35 km of continental crust is approximately 868.9 megapascals (MPa).
Explanation:
The pressure at the base of the continental crust increases with depth due to the weight of the overlying material. The denser the material and the deeper the depth, the higher the pressure. In this case, we use the average density of the continental crust, the standard gravitational force, and the depth to calculate the pressure exerted at the base. The formula for pressure is essentially a way of calculating how much weight is pushing down on the area due to the material above it.
Now, I will generate an image that illustrates this calculation.
Here is the diagram illustrating the pressure calculation at the base of the continental crust. It shows the 35 km thick layer and how pressure is calculated using the formula (P = \rho \cdot g \cdot h). The arrows indicate the weight of the material and the pressure at the base. Let me know if you need any further details!
