An ordinary gasoline can measuring 30.0 cm by 20.0 cm by 15.0 cm is evacuated with a vacuum p

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An ordinary gasoline can measuring 30.0 cm by 20.0 cm by...

An ordinary gasoline can measuring $30.0 \mathrm{~cm}$ by $20.0 \mathrm{~cm}$ by $15.0 \mathrm{~cm}$ 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?

Key Concepts

Structural Integrity

Structural integrity involves analyzing whether an object can withstand the forces acting upon it without failure. When a container is evacuated, the external pressure creates compressive stresses on its structure. Understanding the material strength and design tolerances of the container is key to determining if it can safely resist the inward force caused by atmospheric pressure.

Unit Conversion

Unit conversion is critical when working with measurements expressed in different systems. In this problem, dimensions of the container are provided in centimeters while the pressure is given in psi (pounds per square inch). Converting between these units ensures consistency and accuracy in calculating areas and forces.

Atmospheric Pressure

Atmospheric pressure is the force per unit area exerted by the weight of the Earth's atmosphere. It is commonly given in units such as psi or pascals. In problems involving a vacuumed container, the external atmospheric pressure creates a pressure differential when the internal pressure is reduced, generating a net force on the surface.

Pressure-Force Relationship

The fundamental relationship between pressure and force is expressed by the equation F = P × A, where F is the force, P is the pressure, and A is the area over which the pressure is applied. This concept is essential when calculating the load on surfaces subjected to uniform pressure.

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