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.
What force does this pressure exert on a dart in a 1.4-cm-diameter tube?
Here's the actual answer.
Pressure = Force / Area
Force = Pressure * Area
Area = πr^2
1.4cm = 0.014m
0.014m/2 = 0.007m (this is the radius)
(π)(0.007^2) = 1.54 *10^-4 m^3 (this is the area)
6.0kPa = 6000Pa (this is the force)
(1.54*10^-4 m^3)(6000Pa) = 0.92N (this is the pressure, aka your answer)
To calculate the force exerted on the dart, we can use the formula:
Force = Pressure × Area
Step 1: Convert the gauge pressure to pascal (Pa).
1 kPa = 1000 Pa
So, 6.0 kPa = 6.0 × 1000 Pa = 6000 Pa
Step 2: Calculate the area of the tube.
The diameter of the tube is given as 1.4 cm. We need to convert it to meters (m) since the SI unit of area is square meters (m²).
Radius (r) = Diameter / 2 = 1.4 cm / 2 = 0.7 cm = 0.007 m
Area = π × r²
Area = π × (0.007 m)²
Area ≈ 0.000154 m²
Step 3: Calculate the force exerted.
Force = Pressure × Area
Force = 6000 Pa × 0.000154 m²
Force ≈ 0.924 N
Therefore, the pressure exerted on the dart in a 1.4-cm-diameter tube is approximately 0.924 newtons (N).
Multiply the gauge pressure in Pascals (6000) by the tube's circular inner area cross section in square meters (pi D^2/4) to get the force in Newtons.
pi D^2/4 = 1.54*10-4 m^2
I get about 1 Newton, which is about 1/4 pound force.