Homework Help: Momentum and centre of mass

1. Jun 30, 2008

ace123

Two identical balls, each with velocity v, strike each other at right angles to each other. They stick together. Ignoring friction, (a) describe the motion of the combined ball after the collision and (b) describe the motion of the centre of mass of the two balls before and after the collision.

Not quite sure how to do this but here is what I came up with:

a. If they hit at right angles and stick to each other the will travel in a 45 degree angle from the position of contact? Is this correct?

b. The centre of mass of the each ball will be a straight line prior to contact and a straight line after the collision. Is this correct?

Thanks for the help

2. Jun 30, 2008

Hootenanny

Staff Emeritus
Sounds good
I believe the question wants to know the behaviour of the combined centre of mass of both balls before and after the collision.

3. Jun 30, 2008

ace123

hmm. Well what could be the behavior of the combined centre of mass before the collision? They are moving at rights angles to each other and the centre of mass will be a straight line for each. And then after the collision it will still be a straight line at 45 degrees. How would i describe the combined behaviour prior.

4. Jun 30, 2008

Hootenanny

Staff Emeritus
Notice that the two balls have the same mass. How does one normally add velocities?

5. Jun 30, 2008

ace123

Um you mean like a resultant?

6. Jun 30, 2008

Hootenanny

Staff Emeritus
Yes. The momentum of the centre of mass must be equal to the total momentum of the system.

7. Jun 30, 2008

ace123

So what would i say the motion would be? The resultant of the 2 momentum's?

8. Jun 30, 2008

Hootenanny

Staff Emeritus
Personally, I would determine the velocity of the COM and then simple state that the COM moves with that velocity.

9. Jun 30, 2008

ace123

Is that what the question means by describing the motion? Because I just thought he wanted us to tell him how would the centre of mass move.

10. Jun 30, 2008

ace123

One more question what would the mass be for the centre of mass?

Would it just be 2m?

Would the velocity of the COM be ($$\sqrt{}2$$/2)V?

Thanks

Last edited: Jun 30, 2008
11. Jul 1, 2008

Hootenanny

Staff Emeritus
But doesn't the velocity describe how the centre of mass moves?
Yes, the centre of mass is equivalent to a particle of mass 2m.
That is the correct speed of the centre of mass, but don't forget that velocity is a vector and so a direction is required also.