read below?

Question

A rifle with a mass of 4.0 kg fires a bullet with a mass of 5.5 g (0.0055 kg). The bullet moves with a muzzle velocity of 360 m/s after the rifle is fired.
(a) What is the momentum of the bullet after the rifle is fired?
kgm/s
(b) If external forces acting on the rifle can be ignored, what is the recoil velocity of the rifle?
m/s (in the opposite direction to the bullet)

Answer 1

Slider728 got the first part (bullet momentum) right, but not the second part (recoil velocity of the rifle). His equation for force is incorrect. Energy = mass * velocity ^2 and force is NOT a constant one-half the energy.

The equal and opposite reaction referred to by Newton applies to momentum not to energy, so the velocity is not squared. So V = 1.98Kg*M/S / 4.0Kg = 0.495M/S for the velocity of the rifle (if the weight and velocity of the gases resulting from the burnt powder are ignored). The total momentum summed across all directions of the rifle and the bullet remains 0.0. There is the "Law of Conservation of Momentum", but no "Law of Conservation of Energy" (momentum is directional, energy is not). However since the burnt powder gases are exiting in the same direction as the bullet, the recoil velocity is actually somewhat higher. The amount of the momentum of these gases will be needed to be added to the momentum (in the opposite direction) of the gun in order to get the true velocity of the recoiling gun. This additional momentum can be approximated by the amount of powder in the cartridge being fired times the exit velocity of the bullet. Adding this additional momentum to the 1.98Kg*M/S and dividing the result by the rifle weight will give a corrected estimate of the rifle's recoil velocity.

Answer 2

You might have better luck with answers in the Physics catagory.

Anyway...

a) Momentum (p) = mass (m) * velocity (v).

In the case of the bullet, p=0.0055kg * 360 m/s

p = 1.98 kg*m/s

b) It was Newton that says that every action has an equal but opposite reaction. Thus the force in the bullet must be countered by the same force in the rifle.

Using the equation Force (F) = 1/2 * mass (m) * Velocity (v) ^2

For the bullet... F = 0.5 * 0.0055kg * (360 m/s)^2 = 356.4 N

Using the same question solving for velocity v^2 = 2F/m (remember that "m" is now the mass of the rifle, not the mass of the bullet)

v^2=(2 * 356.4 N) / 4.0 kg= 178.2 (m/s)^2

Taking the square root of both sides of the equation, the velocity of the rifle is:

v = 13.4 m/s