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

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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 will withstand the force?

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 will withstand the force?

Key Concepts

Pressure

Pressure is defined as force applied per unit area. It quantifies the intensity of the force acting perpendicular to a surface. In this context, atmospheric pressure acts on the external surface of the vacuumized can, producing a significant net force due to the absence of counteracting pressure from inside.

Force Calculation from Pressure and Area

The force on a surface can be determined using the relationship F = p × A, where F is the force, p is the pressure, and A is the area over which the pressure acts. This concept is essential to evaluate the total force exerted by atmospheric pressure on the can’s surface when the internal pressure is significantly reduced.

Unit Conversion

Unit conversion is a key concept when working with measurements given in different units, such as converting the dimensions of the can from centimeters to inches to match the pressure unit (psi). Correct unit conversion ensures that calculations of area and subsequent force estimation are accurate.

Structural Integrity Under External Pressure

This concept pertains to assessing whether a structure, like the can, can withstand the forces exerted by external pressure. Understanding material strength and design principles is crucial to determine if the can will fail or remain intact under the high compressive forces resulting from a vacuum inside countered by ambient atmospheric pressure outside.

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