# Homework Help: Center of mass question

1. Jun 30, 2008

### zila24

Consider two identical billiard balls – one with velocity v and the other stationary. They collide with each other. (a) Describe the motion of the two balls after the collision. (b) Describe the motion of the centre of mass of the two balls before the collision. (c) Describe the motion of the centre of mass of the two balls after the collision.

i got the answer to the first part of this question but im having trouble with b and c.

2. Jun 30, 2008

### Hootenanny

Staff Emeritus
Okay, where is the centre of mass located?

3. Jun 30, 2008

### zila24

in the middle of the ball ?

4. Jun 30, 2008

### Hootenanny

Staff Emeritus
Sorry, I meant where is the combined centre of mass of both balls located?

5. Jun 30, 2008

### zila24

would it be half way between them?

6. Jun 30, 2008

### Hootenanny

Staff Emeritus
Correct, the centre of mass of the two balls is at the point half-way between them. So, does this point remain stationary?

7. Jun 30, 2008

### zila24

no as the first ball gets closer, the center of mass chnages to remain in the middle of both...?

8. Jun 30, 2008

### Hootenanny

Staff Emeritus
Correct, so how fast does it change, i.e. at what speed does the centre of mass move?

9. Jun 30, 2008

### zila24

velocity v

10. Jun 30, 2008

### Hootenanny

Staff Emeritus
Correct . The same logic can be applied to answer question (c). Alternatively, since there are no external forces acting on the centre of mass of the system, what can you deduce about it's velocity?

11. Jun 30, 2008

### zila24

since its the other billiard ball that is traveling with a velocity v, now the center of mass is traveling with velocity v

12. Jun 30, 2008

### Hootenanny

Staff Emeritus
Correct . You could have also arrived at the same result by reasoning that since there is no net external force acting on the centre of mass, that it will continue with uniform velocity.

13. Jun 30, 2008

### zila24

thank you...i think i get it... i had another question with a similar problem
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

would the motion be in the resultant vector of the 90 angle?
since they are together would it be in between them at teh same angle and speed?

14. Jun 30, 2008

### Vikingjl11

hootenanny- is the center of mass not moving at (V/2) m/s?

15. Jun 30, 2008

### ace123

Your in my physics class aren't you??

16. Jun 30, 2008

### Hootenanny

Staff Emeritus
Oh my word! I must be half asleep, you are indeed correct Viking! Sorry for the mix up guys, I guess I need some sleep :zzz:.

zila24: To determine the velocity of the centre of mass you need to consider the total momentum of the two balls. This total momentum must be equal to the momentum of the centre of mass. Since you already know the mass of the centre of mass, you should easily be able to determine the velocity, which as Viking correctly says is V/2.

Once again, sorry for the mix-up guys .

17. Jun 30, 2008

### zila24

oh ok... am i right about the second question?
after the collision since they are together where would the CM be and the velocity ?

18. Jun 30, 2008

### zila24

lol ace123 yeaa i just saw ur post

19. Jun 30, 2008

### ace123

Did you know homework 8 is due tommorow as well?

20. Jun 30, 2008

### zila24

yea i just checked my email =/ too much work!