Calculating range with controlled air gun

[Benigna]

Homework Statement

Ultimately, I need to calculate the range of projectile fired from my controlled air gun. My meter gives me pressure in psi which i keep at constant 40 psi, allows me measure (theta) 45 degrees, volume 2.48 in^3

Homework Equations

R=(v^2/g)*sin(2(theta)); x(t)=v cos(theta)t and factored equations that follow

The Attempt at a Solution

Well as you know, most equations solving for range require initial velocity among other things. I can solve for initial velocity easily enough, given mass, time, distance, final velocity, kinetic energy, or any mixture of those. My problem is my meter measures psi. Is there a way to convert psi into energy, use it to solve for initial velocity, or some method that will lead to my range? Please assist if you're online, I have class soon.

 

[tiny-tim]

Welcome to PF!

Hi Benigna! Welcome to PF!

(have a theta: θ and try using the X² icon just above the Reply box )

I'm not sure exactly how a controlled air gun works, but https://www.physicsforums.com/library.php?do=view_item&itemid=80" imparted to the projectile,

so if the pressure P stays the same the full length L of the barrel (does it?), then the initial KE would be PL/A.

 

[Benigna]

Ah i see. You are correct, I did not think to relate my pressure to force and solve for work. Once initial kinetic energy is found in (joules?), i use v1 = sqrt ((2 * e) / m); where e is energy in joules. Then solve for range. Does this seem right?

 

[tiny-tim]

Yup!

 

[paranormal]

Hi there,

I would suggest the following approach to calculate the range of your projectile fired from the controlled air gun:

1. Convert the pressure measurement from psi to its equivalent in Pascals, which is the SI unit for pressure. This can be done by using the conversion factor: 1 psi = 6894.76 Pa.

2. Use the ideal gas law to calculate the volume of gas released from the air gun. The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. Since you have a constant pressure of 40 psi and a known volume of 2.48 in^3, you can calculate the number of moles of gas released.

3. Use the kinetic energy equation, KE = 1/2 mv^2, to calculate the initial velocity of the projectile. You will need to know the mass of the projectile, which can be measured or estimated, and the calculated number of moles of gas.

4. Use the equations you provided (R = (v^2/g)*sin(2(theta)) and x(t) = v cos(theta)t) to calculate the range of the projectile. Keep in mind that the initial velocity calculated in step 3 may not be the same as the actual initial velocity due to factors such as friction and air resistance.

I hope this helps and good luck with your calculations!