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Given a column of air with a pressure of 1.57 x 105 Pa and an area of 1.06 m2 and given that the acceleration due to gravity is 9.8 m/s2, what is the mass of this column?

User Riho
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1 Answer

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The mass of the column of air is approximately \( 16951.02 \, \text{kg} \).

The mass of a column of air can be determined using the formula for pressure:

\[ P = \frac{F}{A} \]

where:

- \( P \) is the pressure,

- \( F \) is the force, and

- \( A \) is the area.

Rearranging the formula to solve for force (\( F \)), we get:

\[ F = P \times A \]

Now, force is related to mass (\( m \)) and acceleration due to gravity (\( g \)) through the equation:

\[ F = m \times g \]

Combining the two equations:

\[ P \times A = m \times g \]

Solving for mass (\( m \)):

\[ m = \frac{P \times A}{g} \]

Substitute the given values:

\[ m = \frac{(1.57 \times 10^5 \, \text{Pa}) \times (1.06 \, \text{m}^2)}{9.8 \, \text{m/s}^2} \]

Now calculate:

\[ m \approx \frac{166220}{9.8} \, \text{kg} \]

\[ m \approx 16951.02 \, \text{kg} \]

So, the mass of the column of air is approximately \( 16951.02 \, \text{kg} \).

User Renaldo
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