Example 11.2 from College Physics, 11.3 Pressure

Calculating Force Exerted by the Air: What Force Does a Pressure Exert?

An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads $6 . 90 \times 10^{6} Pa$ . What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We can find the force exerted from the definition of pressure given in $P = \frac{F}{A}$ , provided we can find the area $A$ acted upon.
Solution
By rearranging the definition of pressure to solve for force, we see that

$F = PA .$
11.10

Here, the pressure $P$ is given, as is the area of the end of the cylinder $A$ , given by $A = {πr}^{2}$ . Thus,

$\begin{array}{l} F & = & (6.90 \times 10^{6} {N/m}^{2}) (3.14) {(0.0750 m)}^{2} \\ = & 1.22 \times 10^{5} N. \end{array}$
11.11
Discussion
Wow! No wonder the tank must be strong. Since we found $F = PA$ , we see that the force exerted by a pressure is directly proportional to the area acted upon as well as the pressure itself.

0 of 3 steps open

How did it go?

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Solution

Discussion

Strategy

Solution

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