Chapter 12: Problem 9
Scientists have found evidence that Mars may once have had an ocean 0.500 km deep. The acceleration due to gravity on Mars is 3.71 m/s\(^2\). (a) What would be the gauge pressure at the bottom of such an ocean, assuming it was freshwater? (b) To what depth would you need to go in the earth's ocean to experience the same gauge pressure?
Short Answer
Step by step solution
Gauge Pressure Formula
Calculate Gauge Pressure on Mars
Finding Equivalent Depth on Earth
Calculate Equivalent Depth on Earth
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Gravity on Mars
Understanding Martian gravity helps scientists predict how objects behave on Mars and is vital for mission planning and scientific calculations, such as pressure in potential ancient Martian oceans.
In summary:
- Mars' gravitational acceleration is 3.71 m/s\(^2\), weaker than Earth's 9.81 m/s\(^2\).
- This weaker gravity influences the pressure exerted by fluids on the Martian surface.
Freshwater Density
When calculating the gauge pressure at the bottom of a body of water, knowing the density is crucial as it affects the result significantly. Denser fluids will exert more pressure, so always using the correct density value is important for accurate results.
For students working with pressure equations:
- Standard freshwater density is usually taken as 1000 kg/m\(^3\).
- Density impacts how fluids exert pressure at a given depth.
Pressure Calculations
This formula helps calculate the pressure within a fluid at any given depth, and is widely used in fluid mechanics. By substituting known values into the formula, students can solve for the gauge pressure in different scenarios, including those on planets with different gravitational forces, like Mars.
Some key points to remember:
- The formula \(P_g = \rho g h\) is used to calculate gauge pressure.
- Substitute known values to find the pressure exerted by a fluid.
- It's applicable even on planets with different gravitational accelerations.
Acceleration Due to Gravity
This value is critical in physics as it affects everything from how objects fall to how pressure is calculated in fluids. On other planets, the acceleration due to gravity could be different. For example, on Mars, gravity is weaker at 3.71 m/s\(^2\).
This discrepancy must be considered in pressure calculations or any situation involving gravitational forces, as it alters how forces, including fluid pressure, are calculated:
- Earth's gravity is 9.81 m/s\(^2\).
- Mars has weaker gravity at 3.71 m/s\(^2\).
- Gravity affects movement, fall rates, and pressure calculations.