What is the Motion of the Center of Mass in a Billiard Ball Collision?

[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 I am having trouble with b and c.

 

[Hootenanny]

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 I am having trouble with b and c.

Okay, where is the centre of mass located?

 

[zila24]

in the middle of the ball ?

 

[Hootenanny]

in the middle of the ball ?

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

 

[zila24]

would it be half way between them?

 

[Hootenanny]

would it be half way between them?

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

 

[zila24]

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

 

[Hootenanny]

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

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

 

[zila24]

velocity v

 

[Hootenanny]

velocity v

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?

 

[zila24]

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

 

[Hootenanny]

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

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.

 

[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?

 

[Vikingjl11]

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

 

[ace123]

Your in my physics class aren't you??

 

[Hootenanny]

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

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 .

 

[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 ?

 

[zila24]

lol ace123 yeaa i just saw ur post

 

[ace123]

Did you know homework 8 is due tommorow as well?

 

[zila24]

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