An ordinary gasoline can measuring 30.0 cm by 20.0 cm by 15.0 cm is evacuated with a vacuum pump. Assuming that virtually all of the air can be removed from inside the can and that atmospheric pressure is 14.7 psi, what is the total force (in pounds) on the surface of the can? Do you think that the can could withstand the force?

검증된 단계별 안내

Calculate the surface area of the can: The can is a rectangular prism, so calculate the surface area by finding the area of each face and summing them up. The formula for the surface area of a rectangular prism is: \$2(lw + lh + wh)$, where $l$, $w$, and $h$ are the length, width, and height of the can.

Convert the dimensions from centimeters to inches: Since the pressure is given in psi (pounds per square inch), convert the dimensions from centimeters to inches using the conversion factor $1 \text{ cm} = 0.393701 \text{ inches}$.

Calculate the total surface area in square inches: Use the converted dimensions to find the surface area in square inches.

Calculate the total force on the surface of the can: Use the formula $\text{Force} = \text{Pressure} \times \text{Area}$, where the pressure is 14.7 psi and the area is the total surface area in square inches.

Consider the structural integrity of the can: Discuss whether the can could withstand the calculated force by considering the material and construction of the can.

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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, atmospheric pressure is given as 14.7 psi, which means that every square inch of the surface area of the can experiences this force due to the weight of the air above it. Understanding pressure is crucial for calculating the total force acting on the can's surface.

Surface Area

The surface area of an object is the total area that the surface of the object occupies. For the gasoline can, the dimensions provided (30.0 cm by 20.0 cm by 15.0 cm) can be used to calculate the total surface area. This area is essential for determining how much force is applied by the atmospheric pressure on the can.

Force Calculation

Force can be calculated using the formula F = P × A, where F is the force, P is the pressure, and A is the area. In this scenario, once the surface area of the can is determined, multiplying it by the atmospheric pressure will yield the total force acting on the can. This calculation is vital to assess whether the can can withstand the resulting force.