What force acted on the bullet while it was moving down the barrel?

[lch20yy]

Homework Statement

a pistol fires a 3-g bullet with a speed of 400 m/s. the pistol barrel is 13 cm long.(a) how much energy is given to the bullet? (b) what average force acted on the bullet while it was moving down the barrel? (c) was this force equal in magnitude to the force of the expanding gases on the bullet?

Homework Equations

The Attempt at a Solution

i have solved a and b. i don't really know how to explain c, does it have anything to do with Newton's third law

 

[PeterO]

Homework Statement

a pistol fires a 3-g bullet with a speed of 400 m/s. the pistol barrel is 13 cm long.(a) how much energy is given to the bullet? (b) what average force acted on the bullet while it was moving down the barrel? (c) was this force equal in magnitude to the force of the expanding gases on the bullet?

Homework Equations

The Attempt at a Solution

i have solved a and b. i don't really know how to explain c, does it have anything to do with Newton's third law

Although we often talk about the average force on the bullet as it moves down the barrel, in reality the force varies. It is zero as the propellant ignites - increases to a maximum as the pressure develops, then reduces as the gas expands into the growing space behind the bullet.
Also, the force of the expanding gases - even if constant - would be, to some extent, opposed by the drag force of the barrel on the bullet - as shown by the spinning of the bullet created by the rifling of the barrel - always assuming Pistols have the spiral grooves in them. never actually seen a pistol close up.

 

[LawrenceC]

Most hand held firearms have rifling that provides 1 rotation of the projectile for every 16inches of barrel length, pistols included. Therefore the kinetic energy imparted to the projectile is greater than the .5mv^2 due to the .5Iw^2.

Some of the energy of the burning propellent is spent propelling itself out of the barrel. With a pistol, say a .45, a typical fully jacketed projectile is around 230 grains (7000 grains in a pound). The powder charge is anywhere from 5 to 10 grains depending on the powder selected.