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Landing on Venus. One of the great difficulties in landing on Venus is dealing with the crushing pressure of the atmosphere, which is 92 times the earth's atmospheric pressure. (a) If you are designing a lander for Venus in the shape of a hemisphere \(2.5 \mathrm{~m}\) in diameter, how many newtons of inward force must it be prepared to withstand due to the Venusian atmosphere? (Don't forget about the bottom!) (b) How much force would the lander have to withstand on the earth?

Short Answer

Expert verified
(a) The lander must withstand approximately 137,230,128 N on Venus. (b) On Earth, the force is about 1,491,632 N.

Step by step solution

01

Calculate the Surface Area of the Hemisphere

We first calculate the surface area of a hemisphere using the formula for the curved surface area: \[ A = 2\pi r^2 \]. The radius \( r \) is half of the diameter: \( r = \frac{2.5}{2} = 1.25 \) m. Substituting in gives \[ A = 2\pi (1.25)^2 \approx 9.81 \text{ m}^2 \].
02

Calculate the Surface Area of the Flat Bottom

The bottom surface is a circle. Its area is given by \( A = \pi r^2 \). Using \( r = 1.25 \) m, we find \[ A = \pi (1.25)^2 \approx 4.91 \text{ m}^2 \].
03

Total Surface Area of the Lander

The total surface area the atmosphere acts upon is the sum of the curved surface and the flat bottom: \[ A_{total} = 9.81 + 4.91 = 14.72 \text{ m}^2 \].
04

Calculate the Pressure on Venus

The pressure on Venus is 92 times the Earth's atmospheric pressure, which is approximately 101,325 Pa (Pascals). \[ P_{Venus} = 92 \times 101,325 = 9,324,900 \text{ Pa} \].
05

Calculate the Force on Venus

The force on the lander on Venus is given by \( F = P \times A \), where \( P \) is the pressure and \( A \) is the total surface area. \[ F = 9,324,900 \times 14.72 \approx 137,230,128 \text{ N} \].
06

Calculate the Pressure on Earth

The pressure on Earth is simply \( P_{Earth} = 101,325 \text{ Pa} \).
07

Calculate the Force on Earth

Using the same formula as before: \( F = P \times A \), for Earth: \[ F = 101,325 \times 14.72 \approx 1,491,632 \text{ N} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atmospheric Pressure
Atmospheric pressure is the force exerted by the weight of the atmosphere on a surface. It acts in all directions and affects everything on the planet, from small objects to large structures. On Earth, this pressure is approximately 101,325 Pascals (Pa) at sea level. However, on other planets, such as Venus, atmospheric pressure can be significantly higher.
For instance, Venus has an atmosphere consisting mainly of carbon dioxide, and its pressure is about 92 times greater than Earth’s. This extreme pressure poses a significant challenge to spacecraft or landers design, requiring them to withstand forces much greater than those experienced on Earth.
When engineers design landers for planets like Venus, they must calculate the amount of pressure it will face and ensure that the structure can endure these intensive conditions. Being able to predict and prepare for these conditions is crucial for successful landings.
Force Calculation
Force is a fundamental concept in physics indicating the interaction that causes an object to change its velocity or shape. The force exerted by an atmosphere on a lander can be calculated using the formula: \[ F = P \times A \]where \( F \) is the force, \( P \) the pressure, and \( A \) the area over which the pressure is applied.
To solve problems involving atmospheric pressure, understanding this formula is key. For our Venus lander scenario, we use the given atmospheric pressure on Venus and the total surface area of the lander to find the force it must withstand. This step-by-step calculation ensures engineers know exactly how strong their lander must be to survive entry into another planet's atmosphere.
Performing force calculations with precision is vital in the engineering and scientific fields, particularly in planetary exploration, where environmental conditions are vastly different from Earth.
Surface Area
Surface area is a measure of how much exposed area an object has. In physical applications, calculating the surface area is important when considering the effects of forces or pressures acting on an object, like a lander.
In our scenario with a Venus lander, we calculate two main areas: the curved surface area of the hemisphere and the flat bottom. For a hemisphere, the formula used is: \[ A = 2\pi r^2 \] where \( r \) is the radius of the hemisphere.
Additionally, we calculate the area of the circular flat bottom with: \[ A = \pi r^2 \] Adding both these areas gives the total surface area exposed to the atmospheric pressure, which is critical in determining the total force exerted on the structure.
Understanding the importance of surface area allows scientists and engineers to design more effective and reliable technology for space exploration.
Planetary Science
Planetary science involves studying planets, moons, and planetary systems. It covers the processes governing them, their atmospheres, and potential for sustaining life. When considering planetary science, understanding each planet’s environment, including atmospheric conditions, is essential for designing technology and missions.
The Venus atmosphere, for example, is dense and hot with massive pressure compared to Earth, presenting unique challenges for exploration missions. Knowledge of these characteristics helps scientists predict potential obstacles and plan accordingly.
Exploration missions to planets like Venus provide valuable insights into atmospheric compositions and dynamics, encouraging advancements in space technology. Engineers and scientists work collectively to understand these environments, ensuring all missions are well-equipped for the planetary challenges they may face.

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Most popular questions from this chapter

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