yimfong said:

#1. If two cars with different masses and traveling with equal speeds in opposite directions collide head-on. Why the cars have equal but opposite momentum changes? Are we sure?

#2. When a bullet is fired from the barrel of a gun, the gun recoils. Can i say that the linear momentum of the bullet has to be conserved? Is there any problem with this explaination?

Thanks

[1] Yes

(a) Let's say there are NO momentum changes. That is, the momentum change for car 1 is zero, that is dM1=0. Similarly, the momentum change for car 2, dM2 is also zero. { dM1 simply stands for deltaM1 or change of momentum for car 1 }

(b) Now, let's say the momentum change of car 1 is not zero; let's say it's some value G, so dM1 = G

Since total momentum has to be conserved, the sum of the change in momentum has to be zero, that is dM1+ dM2 = 0. From this, it's easy to see that dM2 = -G, that is "equal but opposite." Even for case (a) the momentum change, albeit zero, is still equal and opposite.

[2] Yes, there is a problem with this explanation. The linear momentum of the bullet is NOT conserved. Consider a bullet, sitting in the chamber of a gun, happy, "at rest." Then some jerk pulls on the trigger, and accelerates it to over 200 meters/sec. Assume that the bullet's mass remains very much the same. Obviously, there's a huge change in momentum for the bullet.

So, what's the dilly yo? Oh, wait, you're from Hong Kong... nevermind...

The "linear momentum of the bullet DOES NOT 'have' (sic.) to be conserved." The total linear momentum of "THE WHOLE SYSTEM" has to be conserved. For the system you may want to consider the gun and the bullet, and maybe even the person holding the gun. That's reason the gun "kicks" when fired: it's the momentum "balancing itself." If you remember from problem [1], dM1 = -dM2

So, the change in linear momentum for the bullet is equal and opposite for the change in momentum for everything that stays behind.

Try to imagine what happens when the bullet finally lodges into someone's gluteus maximus. Is the momentum conserved?

P.S. Archery is cool. You should do archery. Or hockey.