Question

The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A .30 caliber bullet has mass 7.20×10−3 kg and a speed of 601 m/s relative to the muzzle when fired from a rifle that has mass 3.10 kg . The loosely held rifle recoils at a speed of 1.85 m/s relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

Answer 1

The momentum of the propellant gases can be calculated using the conservation of momentum. The momentum of the bullet and rifle before firing is equal to the momentum of the bullet, rifle, and gases after firing. The momentum of the gases is 10.0742 kg·m/s.

Step-by-step explanation:

The momentum of the propellant gases in a coordinate system attached to the Earth as they leave the muzzle of the rifle can be calculated using the conservation of momentum. The momentum of the bullet and rifle before firing is equal to the momentum of the bullet, rifle, and gases after firing.

The momentum of the bullet is given as (mass of bullet) x (velocity of bullet), which is (7.20 x 10^-3 kg) x (601 m/s) = 4.3392 kg·m/s. The momentum of the rifle is given as (mass of rifle) x (velocity of rifle), which is (3.10 kg) x (-1.85 m/s) = -5.735 kg·m/s (negative because the rifle recoils in the opposite direction).

To find the momentum of the gases, we can use the equation: momentum of gases = -(momentum of bullet + momentum of rifle). Plugging in the values, we have momentum of gases = -(-4.3392 kg·m/s + (-5.735 kg·m/s)) = 10.0742 kg·m/s.

Answer 2

Momentum of propellant will be 1.422 kgm/sec

Step-by-step explanation:

We have given the mass of bullet
`m_(bullet)=7.20* 10^(-3)kg`

Velocity of bullet = 601 m /sec

Velocity of rifle with respect to earth = 1.85 m/sec

So velocity of bullet with respect to earth = 601 - 1.85 = 599.15 m/sec

Mass of rifle
`m_(rifle)=3.10kg`

So momentum of rifle
`P_(rifle)=3.10* 1.85=5.735kgm/sec`

And momentum of bullet
`P_(bullet)=7.2* 10^(-3)* 599.15=4.313kgm/sec`

So the momentum of propellant = momentum of rifle - momentum of bullet = 5.735 -4.313 = 1.422 kgm/sec