Question

When a .22-caliber rifle is fired, the expanding gas from the burning gunpowder creates a pressure behind the bullet. This pressure causes the force that pushes the bullet through the barrel. The barrel has a length of 0.61 m and an opening whose radius is 2.8  103 m. A bullet (mass  2.6  103 kg) has a speed of 370 m/s after passing through this barrel. Ignore friction and determine the average pressure of the expanding gas.

Answer 1

First let's find the acceleration of the bullet
Initial velocity u = 0
final velocity v = 370 m/s
distance x = 0.61m

use v^2 = u^2+2ax
370x370 = 2a.0.62
Giving a = 370x370/ (2 x 0.61) = 112213.11 m/s2

Now, what's the force on the bullet
Force F = Mass m . a
F = 2.6 x 10 -3 x 112213.11
=291.75N

Pressure = Force / Area
Area A = pi r^2 = 3.142 * (2.8x10-3)^2 = 2.46 x 10-5
P = 291.75 / 2.46x10-5
= 1.185 x 10^7 N/m2