# Linear momentum confusion(help required)

1. Aug 8, 2012

### rick2395

There is a line written in my physics text book it says " For any type of collision momentum can be conserved before and after the collision about the line of collision and and about the line perpendicular to the line of collision" . Well i got a question here can we always conserve momentum about the line perpendicular to the line of collision?

Since all this time i knew we could only conserve momentum about the line where no net force is acting.

If two projectiles collide head on in mid air then along the vertical direction i.e along the line perpendicular to the line of collision "mg" is acting Hence net force is not ZERO. So how ?

2. Aug 8, 2012

### Simon Bridge

Welcome to PF;
Momentum is always conserved.
Note - in a collision there are unbalanced forces all over the place ... each object in the collision may change it's momentum, therefore it must have experienced an unbalanced force.

How ... what?
Note: if a projectile falls towards the Earth due to the Earths gravitational pull, the momentum gained is balanced by equal and opposite gain by the Earth being attracted by the projectile.

3. Aug 8, 2012

### Staff: Mentor

One usually assumes that the duration of the collision is short enough that the effect of outside forces (such as gravity) can be ignored during the collision (the contact forces are much greater). This is called the 'impulse approximation' in many textbooks.

4. Aug 9, 2012

### Simon Bridge

That too :) though it is not uncommon for students to face questions involving quite lengthy complicated collisions like car-crashes... then it boils down to what counts as "short enough".

I was concerned at the idea that momentum may not be conserved during the action of an unbalanced force. However, for the colliding-projectiles example, it would be very common to take a "very short collision time" approach and we wouldn't normally factor in the momentum change for the Earth.

The passage that confuses rick2395 is trying to tell him that the components of the total momentum are conserved separately.

5. Aug 9, 2012

### rick2395

Basically as far i am concerned MOMENTUM CAN BE CONSERVED ALONG A DIRECTION WHERE NO NET EXTERNAL FORCE IS ACTING but in the example of the two projectiles force mg of both the particles acts downwards and there is no force to balance them(Unlike if they would have been place on a surface because then the force mg would have been negated by the normal reaction) so a net force mg + mg=2mg is acting along the vertical direction, and i can still conserve momentum along the vertical direction?

6. Aug 9, 2012

### ZapperZ

Staff Emeritus
I'm not sure what the issue is here.

The momentum along the vertical direction is not conserved in your case IF you only consider your system as being the two particles only! The fact that there is an external force acting on the two particles in the vertical direction tells you that the momentum of the 2 particles are not going to be conserved. Your text is describing a system in which no external net force is acting on that system. This is not the case here for the 2 particles.

If you consider the system as being the 2 particles plus the earth, then yes, the momentum of that 3-body system is conserved.

Zz.

7. Aug 9, 2012

### rick2395

i get that.
What changes do i have to make in writing the equation(momentum equations)
if i take into consideration the earth as well??

8. Aug 9, 2012

### ZapperZ

Staff Emeritus
Why can't you just deal with the horizontal component and ignore the vertical component? What is it that you are trying to find?

Zz.