Landing on Venus. One of the great difficulties in landing...

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?

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?

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Key Concepts

Scaling Atmospheric Conditions

Scaling atmospheric conditions involves comparing pressures from different environments, such as Venus and Earth. Understanding that the Venusian atmosphere has a pressure many times that of Earth’s allows engineers to design structures by scaling calculations proportionally, ensuring that materials and designs can withstand extreme conditions.

Surface Area Calculation for Geometric Shapes

Calculating the area of an object’s surface is essential when determining the force due to pressure. For curved surfaces such as a hemisphere, one must account for both the curved portion and any additional 'flat' sections, ensuring that the entire surface exposed to the pressure is included in the calculation.

Atmospheric Pressure

Atmospheric pressure is the force exerted per unit area by the weight of the atmosphere. It is a key concept in understanding how fluid pressures act on surfaces. In problems like this, the pressure (measured in Pascals) multiplied by the area it acts on gives the net force applied to the object.

Force Calculation Using Pressure

Force is calculated by the product of pressure and the area over which it acts (F = P × A). This relationship is central to evaluating how much force a structure must withstand when exposed to different atmospheric pressures on various celestial bodies.

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