Exploring Venus. The surface pressure on Venus is 92 atm, and the acceleration due to gravity there is 0.894g. In a future exploratory mission, an upright cylindrical tank of benzene is sealed at the top but still pressurized at 92 atm just above the benzene. The tank has a diameter of 1.72 m, and the benzene column is 11.50 m tall. Ignore any effects due to the very high temperature on Venus. What force does the Venusian atmosphere exert on the outside surface of the bottom of the tank?

검증된 단계별 안내

First, understand that the force exerted by the Venusian atmosphere on the outside surface of the bottom of the tank is due to the atmospheric pressure acting over the area of the bottom surface.

Calculate the area of the bottom of the cylindrical tank using the formula for the area of a circle: \( A = \pi r^2 \), where \( r \) is the radius of the tank. Given the diameter is 1.72 m, the radius \( r \) is half of that.

Convert the atmospheric pressure from atmospheres to pascals (Pa) for consistency in units. Use the conversion factor: 1 atm = 101325 Pa.

Calculate the force exerted by the atmosphere using the formula: \( F = P \times A \), where \( P \) is the pressure in pascals and \( A \) is the area calculated in step 2.

Substitute the values for pressure and area into the force equation to find the force exerted by the Venusian atmosphere on the bottom of the tank.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Pressure

Pressure is defined as the force exerted per unit area. In this context, the pressure exerted by the Venusian atmosphere is 92 atm, which is significantly higher than Earth's atmospheric pressure. Understanding pressure is crucial for calculating the force exerted on surfaces, as it directly influences the force applied over a given area.

Force

Force is a vector quantity that represents the interaction that changes the motion of an object. It is calculated as the product of pressure and area (F = P × A). In this problem, the force exerted by the atmosphere on the tank's bottom surface is determined by multiplying the atmospheric pressure by the area of the tank's bottom.

Area of a Circle

The area of a circle is calculated using the formula A = πr², where r is the radius of the circle. For the cylindrical tank, the diameter is given as 1.72 m, so the radius is half of that. Calculating the area of the tank's bottom is essential for determining the force exerted by the atmospheric pressure on it.