# Large mass collision momentum problem

1. Jan 18, 2006

When a large mass collides with a small mass, it is slowed down but continues to move in the same direction. However, when a small mass collides with a large one, it bounces backwards in the opposite direction. why?
I understand that the small mass will have a greater change in velocity due to conservation of momentum etc. But what's to say that the small mass could not just stop, and the big mass start moving, but at a slower speed.

2. Jan 18, 2006

### fargoth

i think its a question of how much force is acted on the stationary body when collision occures, and what velocity this force can give to it.

when a body with small mass collides with a large mass body it will gain the bigger mass body little velocity then if the collision was between a moving large mass body and a stationary small mass body.

this can also be viewed considering the center of mass, which will continue to move at the same velocity if the collision was elastic, becuae no external forces act on the system.

Last edited: Jan 18, 2006
3. Jan 18, 2006

### Harmony

This can also be explained through mathematical method.

(m1+m2)v1=(m1-m2)u1+2m2u2

(m1+m2)v2=(m2-m1)u2+2m1u1

When a small mass(m1) collides into a very large mass(m2) which is stationary, m1<<m2 and u2=0.
From the equation, v1=-u1 and v2=0.

The two equations above are derived from canservation of momentum and Newton's Law of Restitution.

4. Jan 18, 2006

### fargoth

dont wanna sound nitpicky, but isnt it conservation of kinetic energy and momentum? you havent entered here the restitution coefficient, so i guess that means it equals 1, in that case its only conservation of kinetic energy...

5. Jan 18, 2006

### Harmony

Well ......To be exact, I was refering to the two equation below:
m1v1+m2v2=m1u1+m2u2

v1-v2=u2-u1

This is only for elastics collision. Since only elastics collision is considered, the coefficient of restitution is 1, as you have said.

6. Jan 18, 2006

### Homer Simpson

This only happens with 'elastic' collision. On a way bigger scale, its the reason a basketball bounces off the earth. When the two collide, they compress together. Then they re-expand. The big one will move a bit, but the small one will really go.