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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 x 10²³ m. A bullet (mass = 2.6 x 10²³ kg) has a speed of 370 m/s after passing through this barrel. Ignore friction and determine the average pressure of the expanding gas.

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Answer:

[tex]1.18454\times 10^{-19}\ Pa[/tex]

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

m = Mass of bullet = [tex]2.6\times 10^{23}\ kg[/tex]

r = Radius of barrel = [tex]2.8\times 10^{23}\ m[/tex]

[tex]v^2-u^2=2as\\\Rightarrow a=\dfrac{v^2-u^2}{2s}\\\Rightarrow a=\dfrac{370^2-0^2}{2\times 0.61}\\\Rightarrow a=112213.11475\ m/s^2[/tex]

Pressure is given by

[tex]P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{ma}{\pi r^2}\\\Rightarrow P=\dfrac{2.6\times 10^{23}\times 112213.11475}{\pi (2.8\times 10^{23})^2}\\\Rightarrow P=1.18454\times 10^{-19}\ Pa[/tex]

The pressure of the expanding gas is [tex]1.18454\times 10^{-19}\ Pa[/tex]