Question

Many cultures around the world still use a simple weapon called a blowgun, a tube with a dart that fits tightly inside. A sharp breath into the end of the tube launches the dart. When exhaling forcefully, a healthy person can supply air at a gauge pressure of 6.0 kPa.
Required:
What force does this pressure exert on a dart in a 1.5-cm-diameter tube?

Answer 1

Answer:

F = 1.06N

Explanation:

In order to calculate the force that produces the given pressure you take into account the following formula:  

$P=\frac{F}{A}$          (1)

P: pressure = 6.0kPa = 6.0*10³ Pa

F: force = ?

A: cross-sectional area of the tube = π r^2

r: radius of the tube = 1.5cm/2 = 0.75cm = 0.75*10^-2 m

You solve the equation (1) for F, and replace the values for the area A and the pressure P:

$F=PA=(6.0*10^{3}Pa)(\pi(0.75*10^{-2}m)^2)\\\\F=1.06N$

The force tha produces a pressure of 6.0kPa in a tube with a diameters of 1.5cm is 1.06N