Pressure, density, and football rules

Classical Mechanics Level 1

Tom's football is found to be inflated at a pressure below the pressure required by the rules. In order to bring the pressure up to the required level, he inflates the ball further. What happens to the density of the air inside the football?

Decreases Unable to be determined Increases Remains the same

July Thomas by July Thomas , 30, USA

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2 solutions

July Thomas
Apr 20, 2016

Relevant wiki: Density

Inflating the ball can only be done by increasing the amount of air inside the football. Since the volume remains constant, the air molecules must become more tightly packed, so the apparent density increases.

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Tom Engelsman
Apr 30, 2021

Per Boyle's Law, the pressure of a gas varies inversely as the volume it occupies: p = k V ⇒ p k = 1 V . \Large p = \frac{k}{V} \Rightarrow \frac{p}{k} = \frac{1}{V}. The density of the gas equals ρ = m V = m p k \Large \rho = \frac{m}{V} = \frac{mp}{k} . Hence, density varies directly as the pressure, which increases as pressure increases.

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