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 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.

Answer 1

`1.18454* 10^(-19)\ Pa`

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

m = Mass of bullet =
`2.6* 10^(23)\ kg`

r = Radius of barrel =
`2.8* 10^(23)\ m`

`v^2-u^2=2as\\\Rightarrow a=(v^2-u^2)/(2s)\\\Rightarrow a=(370^2-0^2)/(2* 0.61)\\\Rightarrow a=112213.11475\ m/s^2`

Pressure is given by

`P=(F)/(A)\\\Rightarrow P=(ma)/(\pi r^2)\\\Rightarrow P=(2.6* 10^(23)* 112213.11475)/(\pi (2.8* 10^(23))^2)\\\Rightarrow P=1.18454* 10^(-19)\ Pa`

The pressure of the expanding gas is
`1.18454* 10^(-19)\ Pa`