# Conservation of momentum when friction is present

Conservation of momentum applies when net force is zero. Suppose that there is a system of a canon and a canonball. Total momentum of the system is zero before canonball is fired. Now canonball is fired from the canon, and in frictionless cases, horizontal-axis momentum of the whole system would be preserved.

Now friction between ground and canon is added. What happens to the momentum of the whole system in this case?

I am confused because for inelastic collsion of the case when a bullet hits a block, it is often said that momentum is preserved during the collision (though not after the collision) even when friction exists between the bullet and the block.

Can I say that friction is negligible at the moment of canonball being fired because $F\Delta t = \Delta p$ would be small as $\Delta t$ is very small?

• Are you talking about the friction between cannonball and the cannon or the friction between cannonball and the target or the cannon and ground? Oct 7 '13 at 7:27
• cannon and ground. Oct 7 '13 at 7:30

However, the mass of the Earth is very large, so the change in velocity is minute. A typical cannonball would have a mass of the order $10\:\mathrm{kg}$. Assuming a muzzle velocity of $100\:\mathrm{m/s}$, the ball gains about $10^3\:\mathrm{kgm/s}$ of momentum. The Earth's momentum therefore changes by the same amount in the opposite direction, but since the Earth's mass is around $6\times 10^{24}\:\mathrm{kg}$, this corresponds to a velocity change of $10^3/6\times 10^{24} \sim 10^{-22}\:\mathrm{m/s}$, which is so small it's effectively unmeasurable.