Calculating Average Pressure in Rifle Barrel from Bullet Launch Speed

[daisyi]

A 0.015 lb. bullet leaves the 23 in. barrel of a 0.30 caliber rifle (whose bore diameter is 0.30 in) at 2000 ft/s. Find the average pressure of the gases in the rifle barrel while the bullet is being accelerated.

 

[AKG]

Given distance, initial velocity, and final velocity, calculate acceleration. Use acceleration and mass to calculate force. Use force and the area of the back of the bullet to calculate pressure. You can figure out how to deal with the ugly units.

P_{avg} = \frac{(0.015\ lb.)\left (\frac{4,000,000\ ft^2/s^2}{46\ in.} \right )}{\pi (0.15\ in.)^2}

 

[daisyi]

Given distance, initial velocity, and final velocity, calculate acceleration. Use acceleration and mass to calculate force. Use force and the area of the back of the bullet to calculate pressure. You can figure out how to deal with the ugly units.

P_{avg} = \frac{(0.015\ lb.)\left (\frac{4,000,000\ ft^2/s^2}{46\ in.} \right )}{\pi (0.15\ in.)^2}

I don't get where you got the 4,000,000 from or the 46 inches.

 

[AKG]

4,000,000 = 2,000² = v² (where v is the final velocity)
46 = 2 x 23 = 2d (where d is the distance travelled)